## what's wrong with LinearSolve?...

following commands on my computer got an error.

restart;
with(LinearAlgebra):
A:=Matrix([[1,3],[2,5]],datatype=float):
b:=Vector([1,1],datatype=float):
LinearSolve(A,b,method=hybrid);
Error, (in SWcallhybrid[1]) param 4 should be an rtable

any suggestion is appreciated.

win7, 12.02

## Quartic equation Solution in Maple...

Dear all,

I want to know how can I solve a fourth or higher order equation to find out its roots, actually coefficients of each power terms itself are functins of other parameters not constant.

Regards.

## How do I restrict input to a function or procedure...

I have a formula, which is called the cube law. It requires input between 0 <= x <= 1. When creating  a procedure I run into all kinds of problems and get nothing but error codes. Trying to use assume works, it puts a tilde mark on the variable x, but doesn't restrict the input. Here is the formula the way it is writtin in a book on calculus:

f(x) := x^3/x^3+(1-x)^3 (0 <= x <= 1).

Trying to restrict the input to be restricted as required by the relational statement has been proven fruitless.

Any help would be greatly appreciated, thanks,

Rolf.

## Error, (in dsolve/numeric/bvp/convertsys) too many...

> restart;
> with(plots);
> Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-2*(diff(f(eta), eta))^2-M^2*(diff(f(eta), eta)) = 0;
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + f(eta) |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d \ 2 / d \
- 2 |----- f(eta)| - M |----- f(eta)| = 0
\ deta / \ deta /
> Eq2 := 1+(4/3)*R*(diff(theta(eta), eta, eta))+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta)) = 0;
4 / d / d \\
1 + - R |----- |----- theta(eta)||
3 \ deta \ deta //

/ / d \ / d \ \
+ Pr |f(eta) |----- theta(eta)| - |----- f(eta)| theta(eta)| = 0
\ \ deta / \ deta / /
> bcs1 := f(0) = S, (D(f))(0) = 1+L*G, (D(D(f)))(0) = .1, f(6) = 0;
f(0) = S, D(f)(0) = 1 + L G, @@(D, 2)(f)(0) = 0.1, f(6) = 0
> fixedparameter := [S = .1, M = .1];
[S = 0.1, M = 0.1]
> Eq3 := eval(Eq1, fixedparameter);
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + f(eta) |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d \ / d \
- 2 |----- f(eta)| - 0.01 |----- f(eta)| = 0
\ deta / \ deta /
> fixedparameter := [R = .1, Pr = .7];
[R = 0.1, Pr = 0.7]
> Eq4 := eval(Eq2, fixedparameter);
/ d / d \\ / d \
1 + 0.1333333333 |----- |----- theta(eta)|| + 0.7 f(eta) |----- theta(eta)|
\ deta \ deta // \ deta /

/ d \
- 0.7 |----- f(eta)| theta(eta) = 0
\ deta /
> bcs2 := theta(0) = 1+T*B, (D(theta))(6) = B, theta(6) = 0;
theta(0) = 1 + T B, D(theta)(6) = B, theta(6) = 0

> T := .1; B := .1;
0.1
0.1
> L := [0., .1, .2, .3];
[0., 0.1, 0.2, 0.3]
> for k to 4 do R := dsolve(eval({Eq3, Eq4, bcs1, bcs2}, L = L[k]), [f(eta), theta(eta)], numeric, output = listprocedure); Y || k := rhs(R[2]); YL || k := rhs(R[3]) end do;
Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 6, got 7
> plot([YL || (1 .. 4)], 0 .. 6, 1 .. -.2, labels = [eta, diff(f(eta), eta)]);

## Error, (in dsolve/numeric/bvp) initial Newton iter...

i am solving 3 ODE with boundary condition.. with boundary condition

b.mw

Maple Worksheet - Error

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

then i got this error

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

i dont know where i need to change.. could you help me..

## abstract algebra sample...

## Error, (in dsolve/numeric/bvp) initial Newton iter...

i am solving 3 ODE question with boundary condition. when i running the programm i got this error.. any one could help me please.. :)

 >
 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
 >
 (5)
 >
 Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging
 >
 (6)
 >
 Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
 >

## A major-league pitcher ...

A major-league pitcher releases a ball at a point 6 feet above the ground and 58 feet from home plate at a speed of 100 mi/hr ,

If gravity had no effect, the ball would travel along a line and cross home plate 4 feet off the ground. Find the drop D caused by gravity.

NB: in this problem the angle alpha is the angle between the horizontal and the direction of the released ball. Since the ball is dropping, alpha will be negative.

## EUREKA ! (shouted Archimedes)...

Archimedes supposedlly, was asked to determine whether a crown made for the king consisted of pure gold. According to

legend, he solved this problem by weighing the crown first in air and then in water. Suppose the scale read 7.84 N when the

crown was in the air and 6.84 N when it was in water.

What should Archimedes have told the king ?

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