Also available:

## How to fix the behaviour of the LinearAlgebra[Eige...

In Maple18.02:

Hso := Matrix(8, {(1, 4) = -x, (1, 6) = I*x, (2, 3) = x, (2, 5) = I*x, (3, 2) = x, (3, 5) = -I*z, (3, 8) = y, (4, 1) = -x, (4, 6) = I*z, (4, 7) = -y, (5, 2) = -I*x, (5, 3) = I*z, (5, 8) = -I*y, (6, 1) = -I*x, (6, 4) = -I*z, (6, 7) = -I*y, (7, 4) = -y, (7, 6) = I*y, (8, 3) = y, (8, 5) = I*y})

av, AV := LinearAlgebra[Eigenvectors](Hso)

Error, (in Polynomial:-Quadratic) type `truefalseFAIL` does not exist

This does not happen in Maple17.

## How to get a numerical answer using the erf functi...

I didn't even know the erf function existed until doing this problem. I looked up how to use it, so I tried plugging in the explicity form into Maple, hoping it'd solve it, but it just spit back out the erf function.

I am trying to get a number answer.  A decimal. Because this is calculating a probability. How do I get Maple to give me a number here? Thanks!

## How to catch Maple Error?...

Sometimes I got an error (purple in output). How can I catch on programming level?

I mean I want to do smth like: if <error> -> then <action>

## How to catch Maple Error?...

Sometimes I got an error (purple in output). How can I catch on programming level?

I mean I want to do smth like: if <error> -> then <action>

## Getting the error of "Error, (in simplify/table) t...

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Question.mw .

Hello, Maple is giving me the error:

"Error, (in simplify/table) too many levels of recursion"

Once I take the integral of an expression I am getting the error. It starts at the first integral of the document.

Note: If I make another maple worksheet and write the expression of the integral without writing it shorthand by substituting the functions in it seems to give me an answer.

For example instead of the integral of say, y(x)*f(x) I would write out the definitions of the functions in the integral and it would give me an answer while the former would give me the error.

I have uploaded the document, Any help would be appreciated. I'm not sure if there is a fix or not. Thanks

## Why is Determinant often incorrect for matrices wi...

When I use the Determinant function on a matrix with (single variable) polynomial entries with real coefficients I often get an incorrect answer. I know the answers are incorrect because they have a higher degree or a lower lowest degree than is possible given the matrix elements.

However, when I replace the coefficients in the polynomials with rational numbers or I put in the option method=minor, I get the correct answer.

The problem seems to be roundoff error. However, the important error is not simply small changes in the resulting polynomial. The important error is the presence of entirely incorrect powers of the variable and not with very small coefficients.

How does this happen and why does the help page for Determinant( ) not warn of this behavior? In particuiar, why does the help page not say that using Gaussian elimination (i.e., the default) will often give incorrect answers in such cases, but using method=minor will work? Is this behavior known? I cannot find any reference to it on the internet.

## Error, too many levels of recursion...

In Maple V, Release 4 (1996):

 T:=table():i:=1:N:=5000;for i from i to N  do   T[i]:=T[i+1]:   T[i+1]:=1;   eval(T[1]);od:print(i);for i from i to N  do   T[i]:=T[i+1]:   T[i+1]:=1;   eval(T[1]);od:print(i);

N := 5000
Error, too many levels of recursion
3607
5001

Can You explain this occurence, as well as the following one:

In Maple V, Release 4 (1996):

 T:=table():i:=1:N:=5000;for i from i to N  do  T[i]:=T[i+1]:  eval(T[1]);od:print(i); for i from i to N  do  T[i]:=T[i+1]:  eval(T[1]);od:print(i);;

gives:

N := 5000
Error, too many levels of recursion
3607
Error, too many levels of recursion
3607

How does one control allowance for recursion depth?

## Error, (in Engine:-Dispatch) not implemented yet: ...

sorry what is what dispatch and implementing what? i get these every week for a number of cases sometimes it specifies that it is an "unhandled psi case" still waiting on that built in proc u guys where gonna dispatch like u know the reasons ppl always have a whinge about evalf not working in some cases  anyway a few people have run into these error id say.

## "solve((x+exp(-1))^x = 1, x)" gives error...

The code "solve((x+exp(-1))^x = 1, x)"gives the error "Error, (in Engine:-Dispatch) invalid subscript selector". How is this possible?

## error ''"initial Newton iteration is not convergin...

"initial Newton iteration is not converging"

thanks..

 (1)

 (2)

 (3)

## Errors in code ...

i encounter with error''

Error, (in StringTools:-IsPrefix) second argument must be a string''

equations which be solved attached as pdf file

thanks

root.pdf

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Constants

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## Problem with odeplot...

Hello,

I tried to plot the problem presented below:

restart; with(plots); C := setcolors(); with(LinearAlgebra);

formula1 := 2.6*BodyWeight*abs(sin(4*Pi*t));
2.6 BodyWeight |sin(4 Pi t)|
BodyWeight := 80*9.81;
plot(formula1, t = 0 .. 2);

eq2 := formula1-SpringConstant*y(t)-DampConstant*(diff(y(t), t)) = Mass*(diff(y(t), `\$`(t, 2)));
2040.480 |sin(4 Pi t)| - SpringConstant y(t)

/ d \ / d / d \\
- DampConstant |--- y(t)| = Mass |--- |--- y(t)||
\ dt / \ dt \ dt //
DampConstant := 50;
50
Mass := .200;
Springt := 200;
200
SpringConstant := Youngsmodulus*Surface/DeltaLength;
DeltaLength := 0.2e-1-y(t);
Surface := .15;
Youngsmodulus := 6.5*10^6/(t+1)+6.5*10^6;
plot(Youngsmodulus, t = 0 .. 10000);

eq2;
2040.480 |sin(4 Pi t)|

/ 6 \
|6.5000000 10 6|
0.15 |------------- + 6.5000000 10 | y(t)
\ t + 1 / / d \
- ----------------------------------------- - 50 |--- y(t)| =
0.02 - y(t) \ dt /

/ d / d \\
0.200 |--- |--- y(t)||
\ dt \ dt //

incs := y(0) = 0, (D(y))(0) = 0;
eq4 := dsolve({eq2, incs}, y(t), type = numeric, method = lsode[backfull], maxfun = 0);
proc(x_lsode) ... end;

plots:-odeplot(eq4, [t, y(t)], 0 .. 5);

When I try to plot it beyond t=5, Maple gives the following error:

Warning, could not obtain numerical solution at all points, plot may be incomplete

Does anyone know how to plot it even further?

## How to solve BVP by shooting method?...

Hi everyone,

I'm kinda new here, and I really hope you guys can help me through this. In my new case study, after some revision, i thought i might be trying to implement a shooting method. I tried my best to make it work/understand but i couldn't get to any result.

So, as attached (i re-do PV Satya Naraya's paper first to be more understand but .....)

Here is my questions and the worksheet:

1) really stuck in mind - what is the purpose of shooting method for some related study?

2) what is the meaning of error .............'use midpoint method intead"

3) Worksheet - 1MASS_JEFF_SATYA_on_Beta.mw

Thanks in advanced. Really hope that someone can help/teach me how to solve the boundary value problem by shooting method.

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## Problem with ODE system...

Hi, i am trying to solve my PDEs with HPM method ,but i get strange errors.

first one is :Error, (in trig/reduce/reduce) Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc,

but when i run my last function again,the error chages,let me show you.

restart;
lambda:=0.5;K[r]:=0.5;Sc:=0.5;Nb:=0.1;Nt:=0.1;Pr:=10;
0.5
0.5
0.5
0.1
0.1
10
> EQUATIONS;

equ1:=diff(f(eta),eta\$4)-R*(diff(f(eta),eta)*diff(f(eta),eta\$2)-f(eta)*diff(f(eta),eta\$2))-2*K[r]*diff(g(eta),eta)=0;

equ2:=diff(g(eta),eta\$2)-R*(diff(f(eta),eta)*g(eta)-f(eta)*diff(g(eta),eta))+2*K[r]*diff(f(eta),eta)=0;

equ3:=diff(theta(eta),eta\$2)+Pr*R*f(eta)*diff(theta(eta),eta)+Nb*diff(phi(eta),eta)*diff(theta(eta),eta)+Nt*diff(theta(eta),eta)^2=0;

equ4:=diff(phi(eta),eta\$2)+R*Sc*f(eta)*diff(phi(eta),eta)+diff(theta(eta),eta\$2)*(Nt/Nb)=0;
/  d   /  d   /  d   /  d         \\\\     //  d         \ /  d
|----- |----- |----- |----- f(eta)|||| - R ||----- f(eta)| |-----
\ deta \ deta \ deta \ deta       ////     \\ deta       / \ deta

/  d         \\          /  d   /  d         \\\
|----- f(eta)|| - f(eta) |----- |----- f(eta)|||
\ deta       //          \ deta \ deta       ///

/  d         \
- 1.0 |----- g(eta)| = 0
\ deta       /
/  d   /  d         \\
|----- |----- g(eta)||
\ deta \ deta       //

//  d         \                 /  d         \\
- R ||----- f(eta)| g(eta) - f(eta) |----- g(eta)||
\\ deta       /                 \ deta       //

/  d         \
+ 1.0 |----- f(eta)| = 0
\ deta       /
/  d   /  d             \\               /  d             \
|----- |----- theta(eta)|| + 10 R f(eta) |----- theta(eta)|
\ deta \ deta           //               \ deta           /

/  d           \ /  d             \
+ 0.1 |----- phi(eta)| |----- theta(eta)|
\ deta         / \ deta           /

2
/  d             \
+ 0.1 |----- theta(eta)|  = 0
\ deta           /
/  d   /  d           \\                /  d           \
|----- |----- phi(eta)|| + 0.5 R f(eta) |----- phi(eta)|
\ deta \ deta         //                \ deta         /

/  d   /  d             \\
+ 1.000000000 |----- |----- theta(eta)|| = 0
\ deta \ deta           //
> BOUNDARY*CONDITIONS;

ics:=
f(0)=0,D(f)(0)=1,g(0)=0,theta(0)=1,phi(0)=1;
f(1)=lambda,D(f)(1)=0,g(1)=0,theta(1)=0,phi(1)=0;
f(0) = 0, D(f)(0) = 1, g(0) = 0, theta(0) = 1, phi(0) = 1
f(1) = 0.5, D(f)(1) = 0, g(1) = 0, theta(1) = 0, phi(1) = 0
> HPMs;

hpm1:=(1-p)*(diff(f(eta),eta\$4)-2*K[r]*diff(g(eta),eta))+p*(diff(f(eta),eta\$4)-R*(diff(f(eta),eta)*diff(f(eta),eta\$2)-f(eta)*diff(f(eta),eta\$2))-2*K[r]*diff(g(eta),eta))=0;

hpm2:=(1-p)*(diff(g(eta),eta\$2)+2*K[r]*diff(f(eta),eta))+p*(diff(g(eta),eta\$2)-R*(diff(f(eta),eta)*g(eta)-f(eta)*diff(g(eta),eta))+2*K[r]*diff(f(eta),eta))=0;

hpm3:=(1-p)*(diff(theta(eta),eta\$2))+p*(diff(theta(eta),eta\$2)+Pr*R*f(eta)*diff(theta(eta),eta)+Nb*diff(phi(eta),eta)*diff(theta(eta),eta)+Nt*diff(theta(eta),eta)^2)=0;

hpm4:=(1-p)*(diff(phi(eta),eta\$2)+diff(theta(eta),eta\$2)*(Nt/Nb))+p*(diff(phi(eta),eta\$2)+R*Sc*f(eta)*diff(phi(eta),eta)+diff(theta(eta),eta\$2)*(Nt/Nb))=0;

//  d   /  d   /  d   /  d         \\\\
(1 - p) ||----- |----- |----- |----- f(eta)||||
\\ deta \ deta \ deta \ deta       ////

/  d         \\     //  d   /  d   /  d   /  d         \
- 1.0 |----- g(eta)|| + p ||----- |----- |----- |----- f(eta)|
\ deta       //     \\ deta \ deta \ deta \ deta       /

\\\     //  d         \ /  d   /  d         \\
||| - R ||----- f(eta)| |----- |----- f(eta)||
///     \\ deta       / \ deta \ deta       //

/  d   /  d         \\\       /  d         \\
- f(eta) |----- |----- f(eta)||| - 1.0 |----- g(eta)|| = 0
\ deta \ deta       ///       \ deta       //
//  d   /  d         \\       /  d         \\     //  d
(1 - p) ||----- |----- g(eta)|| + 1.0 |----- f(eta)|| + p ||-----
\\ deta \ deta       //       \ deta       //     \\ deta

/  d         \\
|----- g(eta)||
\ deta       //

//  d         \                 /  d         \\
- R ||----- f(eta)| g(eta) - f(eta) |----- g(eta)||
\\ deta       /                 \ deta       //

/  d         \\
+ 1.0 |----- f(eta)|| = 0
\ deta       //
/
/  d   /  d             \\     |/  d   /  d             \
(1 - p) |----- |----- theta(eta)|| + p ||----- |----- theta(eta)|
\ deta \ deta           //     \\ deta \ deta           /

\               /  d             \
| + 10 R f(eta) |----- theta(eta)|
/               \ deta           /

/  d           \ /  d             \
+ 0.1 |----- phi(eta)| |----- theta(eta)|
\ deta         / \ deta           /

2\
/  d             \ |
+ 0.1 |----- theta(eta)| | = 0
\ deta           / /
//  d   /  d           \\
(1 - p) ||----- |----- phi(eta)||
\\ deta \ deta         //

/  d   /  d             \\\     //  d   /  d
+ 1.000000000 |----- |----- theta(eta)||| + p ||----- |-----
\ deta \ deta           ///     \\ deta \ deta

\\                /  d           \
phi(eta)|| + 0.5 R f(eta) |----- phi(eta)|
//                \ deta         /

/  d   /  d             \\\
+ 1.000000000 |----- |----- theta(eta)||| = 0
\ deta \ deta           ///
f(eta)=sum(f[i](eta)*p^i,i=0..1);
f(eta) = f[0](eta) + f[1](eta) p
g(eta)=sum(g[i](eta)*p^i,i=0..1);
g(eta) = g[0](eta) + g[1](eta) p
theta(eta)=sum(theta[i](eta)*p^i,i=0..1);
theta(eta) = theta[0](eta) + theta[1](eta) p
phi(eta)=sum(phi[i](eta)*p^i,i=0..1);
phi(eta) = phi[0](eta) + phi[1](eta) p
> FORequ1;

A:=collect(expand(subs(f(eta)=f[0](eta)+f[1](eta)*p,g(eta)=g[0](eta)+g[1](eta)*p,hpm1)),p);
/      /  d            \ /  d   /  d            \\
|-1. R |----- f[1](eta)| |----- |----- f[1](eta)||
\      \ deta          / \ deta \ deta          //

/  d   /  d            \\\  3   /
+ R f[1](eta) |----- |----- f[1](eta)||| p  + |
\ deta \ deta          ///      \
/  d            \ /  d   /  d            \\
-1. R |----- f[0](eta)| |----- |----- f[1](eta)||
\ deta          / \ deta \ deta          //

/  d            \ /  d   /  d            \\
- 1. R |----- f[1](eta)| |----- |----- f[0](eta)||
\ deta          / \ deta \ deta          //

/  d   /  d            \\
+ R f[0](eta) |----- |----- f[1](eta)||
\ deta \ deta          //

/  d   /  d            \\\  2   //  d   /  d   /
+ R f[1](eta) |----- |----- f[0](eta)||| p  + ||----- |----- |
\ deta \ deta          ///      \\ deta \ deta \

d   /  d            \\\\       /  d            \
----- |----- f[1](eta)|||| - 1.0 |----- g[1](eta)|
deta \ deta          ////       \ deta          /

/  d            \ /  d   /  d            \\
- 1. R |----- f[0](eta)| |----- |----- f[0](eta)||
\ deta          / \ deta \ deta          //

/  d   /  d            \\\
+ R f[0](eta) |----- |----- f[0](eta)||| p
\ deta \ deta          ///

/  d   /  d   /  d   /  d            \\\\
+ |----- |----- |----- |----- f[0](eta)||||
\ deta \ deta \ deta \ deta          ////

/  d            \
- 1.0 |----- g[0](eta)| = 0
\ deta          /
A1:=diff(f[0](eta),eta\$4)-2*K[r]*(diff(g[0](eta),eta))=0;
A2:=diff(f[1](eta),eta\$4)-2*K[r]*(diff(g[1](eta),eta))-R*(diff(f[0](eta),eta))*(diff(f[0](eta),eta\$2))+R*f[0](eta)*(diff(f[0](eta),eta\$2))=0;
/  d   /  d   /  d   /  d            \\\\       /  d            \
|----- |----- |----- |----- f[0](eta)|||| - 1.0 |----- g[0](eta)| =
\ deta \ deta \ deta \ deta          ////       \ deta          /

0
/  d   /  d   /  d   /  d            \\\\       /  d            \
|----- |----- |----- |----- f[1](eta)|||| - 1.0 |----- g[1](eta)|
\ deta \ deta \ deta \ deta          ////       \ deta          /

/  d            \ /  d   /  d            \\
- R |----- f[0](eta)| |----- |----- f[0](eta)||
\ deta          / \ deta \ deta          //

/  d   /  d            \\
+ R f[0](eta) |----- |----- f[0](eta)|| = 0
\ deta \ deta          //
icsA1:=f[0](0)=0,D(f[0])(0)=1,g[0](0)=0,f[0](1)=lambda,D(f[0])(1)=0,g[0](1)=0;
icsA2:=f[1](0)=0,D(f[1])(0)=0,g[1](0)=0,f[1](1)=0,D(f[1])(1)=0,g[1](1)=0;
f[0](0) = 0, D(f[0])(0) = 1, g[0](0) = 0, f[0](1) = 0.5,

D(f[0])(1) = 0, g[0](1) = 0
f[1](0) = 0, D(f[1])(0) = 0, g[1](0) = 0, f[1](1) = 0,

D(f[1])(1) = 0, g[1](1) = 0
>
FORequ2;

B:=collect(expand(subs(f(eta)=f[0](eta)+f[1](eta)*p,g(eta)=g[0](eta)+g[1](eta)*p,hpm2)),p);
/      /  d            \
|-1. R |----- f[1](eta)| g[1](eta)
\      \ deta          /

/  d            \\  3   /
+ R f[1](eta) |----- g[1](eta)|| p  + |
\ deta          //      \
/  d            \
-1. R |----- f[0](eta)| g[1](eta)
\ deta          /

/  d            \
- 1. R |----- f[1](eta)| g[0](eta)
\ deta          /

/  d            \
+ R f[0](eta) |----- g[1](eta)|
\ deta          /

/  d            \\  2   //  d   /  d
+ R f[1](eta) |----- g[0](eta)|| p  + ||----- |----- g[1](eta)
\ deta          //      \\ deta \ deta

\\       /  d            \        /  d            \
|| + 1.0 |----- f[1](eta)| - 1. R |----- f[0](eta)| g[0](eta)
//       \ deta          /        \ deta          /

/  d            \\     /  d   /  d            \\
+ R f[0](eta) |----- g[0](eta)|| p + |----- |----- g[0](eta)||
\ deta          //     \ deta \ deta          //

/  d            \
+ 1.0 |----- f[0](eta)| = 0
\ deta          /
B1:=diff(g[0](eta),eta\$2)+2*K[r]*(diff(f[0](eta),eta))=0;
B2:=diff(g[1](eta),eta\$2)+2*K[r]*(diff(f[1](eta),eta))-R*(diff(f[0](eta),eta))*g[0](eta)+R*f[0](eta)*(diff(g[0](eta),eta))=0;
/  d   /  d            \\       /  d            \
|----- |----- g[0](eta)|| + 1.0 |----- f[0](eta)| = 0
\ deta \ deta          //       \ deta          /
/  d   /  d            \\       /  d            \
|----- |----- g[1](eta)|| + 1.0 |----- f[1](eta)|
\ deta \ deta          //       \ deta          /

/  d            \
- R |----- f[0](eta)| g[0](eta)
\ deta          /

/  d            \
+ R f[0](eta) |----- g[0](eta)| = 0
\ deta          /
icsB1:=f[0](0)=0,D(f[0])(0)=1,g[0](0)=0,f[0](1)=lambda,D(f[0])(1)=0,g[0](1)=0;
icsB2:=f[1](0)=0,D(f[1])(0)=0,g[1](0)=0,f[1](1)=0,D(f[1])(1)=0,g[1](1)=0;
f[0](0) = 0, D(f[0])(0) = 1, g[0](0) = 0, f[0](1) = 0.5,

D(f[0])(1) = 0, g[0](1) = 0
f[1](0) = 0, D(f[1])(0) = 0, g[1](0) = 0, f[1](1) = 0,

D(f[1])(1) = 0, g[1](1) = 0
> FORequ3;

C:=collect(expand(subs(theta(eta)=theta[0](eta)+theta[1](eta)*p,phi(eta)=phi[0](eta)+phi[1](eta)*p,f(eta)=f[0](eta)+f[1](eta)*p,hpm3)),p);
/
|                /  d                \
|10. R f[1](eta) |----- theta[1](eta)|
\                \ deta              /

/  d              \ /  d                \
+ 0.1 |----- phi[1](eta)| |----- theta[1](eta)|
\ deta            / \ deta              /

2\
/  d                \ |  3   /                /  d
+ 0.1 |----- theta[1](eta)| | p  + |10. R f[0](eta) |-----
\ deta              / /      \                \ deta

\                   /  d                \
theta[1](eta)| + 10. R f[1](eta) |----- theta[0](eta)|
/                   \ deta              /

/  d              \ /  d                \
+ 0.1 |----- phi[0](eta)| |----- theta[1](eta)|
\ deta            / \ deta              /

/  d              \ /  d                \
+ 0.1 |----- phi[1](eta)| |----- theta[0](eta)|
\ deta            / \ deta              /

/
/  d                \ /  d                \\  2   |/
+ 0.2 |----- theta[0](eta)| |----- theta[1](eta)|| p  + ||
\ deta              / \ deta              //      \\

d   /  d                \\
----- |----- theta[1](eta)||
deta \ deta              //

/  d                \
+ 10. R f[0](eta) |----- theta[0](eta)|
\ deta              /

/  d              \ /  d                \
+ 0.1 |----- phi[0](eta)| |----- theta[0](eta)|
\ deta            / \ deta              /

2\
/  d                \ |
+ 0.1 |----- theta[0](eta)| | p
\ deta              / /

/  d   /  d                \\
+ |----- |----- theta[0](eta)|| = 0
\ deta \ deta              //
C1:=diff(theta[0](eta),eta\$2)=0;
C2:=diff(theta[1](eta), eta, eta)+Pr*R*f[0](eta)*(diff(theta[0](eta), eta))+Nb*(diff(phi[0](eta), eta))*(diff(theta[0](eta), eta))+Nt*(diff(theta[0](eta), eta))^2=0;
d   /  d                \
----- |----- theta[0](eta)| = 0
deta \ deta              /
/  d   /  d                \\
|----- |----- theta[1](eta)||
\ deta \ deta              //

/  d                \
+ 10 R f[0](eta) |----- theta[0](eta)|
\ deta              /

/  d              \ /  d                \
+ 0.1 |----- phi[0](eta)| |----- theta[0](eta)|
\ deta            / \ deta              /

2
/  d                \
+ 0.1 |----- theta[0](eta)|  = 0
\ deta              /
icsC1:=theta[0](0)=1,theta[0](1)=0;
icsC2:=theta[1](0)=0,theta[1](1)=0,phi[0](0)=0,phi[0](1)=0;
theta[0](0) = 1, theta[0](1) = 0
theta[1](0) = 0, theta[1](1) = 0, phi[0](0) = 0, phi[0](1) = 0
> FORequ4;

E:=collect(expand(subs(theta(eta)=theta[0](eta)+theta[1](eta)*p,phi(eta)=phi[0](eta)+phi[1](eta)*p,f(eta)=f[0](eta)+f[1](eta)*p,hpm4)),p);
3 /  d              \   /                /  d
0.5 R f[1](eta) p  |----- phi[1](eta)| + |0.5 R f[0](eta) |-----
\ deta            /   \                \ deta

\                   /  d              \\  2   //
phi[1](eta)| + 0.5 R f[1](eta) |----- phi[0](eta)|| p  + ||
/                   \ deta            //      \\

d   /  d              \\
----- |----- phi[1](eta)||
deta \ deta            //

/  d   /  d                \\
+ 1.000000000 |----- |----- theta[1](eta)||
\ deta \ deta              //

/  d              \\
+ 0.5 R f[0](eta) |----- phi[0](eta)|| p
\ deta            //

/  d   /  d              \\
+ |----- |----- phi[0](eta)||
\ deta \ deta            //

/  d   /  d                \\
+ 1.000000000 |----- |----- theta[0](eta)|| = 0
\ deta \ deta              //
E1:=diff(phi[0](eta),eta\$2)+Nt*(diff(theta[0](eta),eta\$2))/Nb=0;
E2:=diff(phi[1](eta),eta\$2)+Nt*(diff(theta[1](eta),eta\$2))/Nb+R*Sc*f[0](eta)*(diff(phi[0](eta),eta))=0;
/  d   /  d              \\
|----- |----- phi[0](eta)||
\ deta \ deta            //

/  d   /  d                \\
+ 1.000000000 |----- |----- theta[0](eta)|| = 0
\ deta \ deta              //
/  d   /  d              \\
|----- |----- phi[1](eta)||
\ deta \ deta            //

/  d   /  d                \\
+ 1.000000000 |----- |----- theta[1](eta)||
\ deta \ deta              //

/  d              \
+ 0.5 R f[0](eta) |----- phi[0](eta)| = 0
\ deta            /
icsE1:=theta[0](0)=1,theta[0](1)=0,phi[0](0)=1,phi[0](1)=0;
icsE2:=theta[1](0)=0,theta[1](1)=0,phi[1](0)=0,phi[1](1)=0;
theta[0](0) = 1, theta[0](1) = 0, phi[0](0) = 1, phi[0](1) = 0
theta[1](0) = 0, theta[1](1) = 0, phi[1](0) = 0, phi[1](1) = 0

theta[0](eta) = -(152675527/100000000)*eta+1;
152675527
theta[0](eta) = - --------- eta + 1
100000000
U:=f[1](eta)=0;
f[1](eta) = 0
Dsolve(A1,B1,icsA1,icsB1);
Dsolve(A1, B1, icsA1, icsB1)

sys:={ diff(g[0](eta), eta, eta)+1.0*(diff(f[0](eta), eta)) = 0, diff(f[0](eta), eta, eta, eta, eta)-1.0*(diff(g[0](eta), eta)) = 0};
//  d   /  d   /  d   /  d            \\\\
{ |----- |----- |----- |----- f[0](eta)||||
\\ deta \ deta \ deta \ deta          ////

/  d            \
- 1.0 |----- g[0](eta)| = 0,
\ deta          /

/  d   /  d            \\       /  d            \    \
|----- |----- g[0](eta)|| + 1.0 |----- f[0](eta)| = 0 }
\ deta \ deta          //       \ deta          /    /
IC_1:={ f[0](0) = 0, (D(f[0]))(0) = 1, g[0](0) = 0, f[0](1) = .5, (D(f[0]))(1) = 0, g[0](1) = 0,f[0](0) = 0, (D(f[0]))(0) = 1, g[0](0) = 0, f[0](1) = .5, (D(f[0]))(1) = 0, g[0](1) = 0};
{f[0](0) = 0, f[0](1) = 0.5, g[0](0) = 0, g[0](1) = 0,

D(f[0])(0) = 1, D(f[0])(1) = 0}
ans1 := combine(dsolve(sys union IC_1,{f[0](eta),g[0](eta)}),trig);
Error, (in dsolve) expecting an ODE or a set or list of ODEs. Received `union`(IC_1, sys)
>

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