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Question: what is the correct syntax for setting initial condition y'(a)=b for an ode?

Question:what is the correct syntax for setting initial condition y'(a)=b for an ode?

nm 9934 Maple 2024
syntax dsolve differential-equations
August 26 2024
2

I sort of remember there is a special syntax for setting initial condition for an ode derivative as    y'(a)=b, where a and b are symbols. I forgot what it is, everything I try gives error. (I thought eval was used to work for this, but can't get it to work now).

Any one knows how to set this IC?   For an example, given this ode y''(x)+y'(x)+y(x)=0 I want to solve it with the IC as   y'(a)=b where a has no numerical value. Just a symbol.

For an example, using another software, it is done as follows

ClearAll[x,y,a,b];
ode=y''[x]+y'[x]+y[x]==0;
DSolve[{ode,y'[a]==b},y[x],x]

Below is my attempts in Maple. I tried eval, subs, and the normal D(y)(a)=b but none of these works when a is symbol. 

I looked at help and all examples I saw use constants, as in D(y)(0)=value. 

Iam sure this is possible to do in Maple, but I forgot how. Below is worksheet.
 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

restart;
> 

ode:=diff(y(x),x$2)+diff(y(x),x)+y(x)=0;
IC1:=eval(diff(y(x),x),x=a)=b;
IC2:=D(y)(a)=b;
IC3:=subs(x=a,D(y)(x)=b);

diff(diff(y(x), x), x)+diff(y(x), x)+y(x) = 0

diff(y(a), a) = b

(D(y))(a) = b

(D(y))(a) = b

> 

dsolve([ode,IC1]);

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(a), y(x)}

> 

dsolve([ode,IC2]);

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(a), y(x)}

> 

dsolve([ode,IC3]);

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(a), y(x)}

> 

#eval works if the point is actual value as in
IC1:=eval(diff(y(x),x),x=0)=b;

eval(diff(y(x), x), {x = 0}) = b

> 

#but I want x=a in the above.


Download how_to_set_IC_point_to_symbol.mw

There is no issue for dirichlet initial condition, where  y(a)=b works. It is the  neumann one which I can't figure its syntax. So this works OK

ode:=diff(y(x),x$2)+diff(y(x),x)+y(x)=0;
IC1:=y(a)=b;
dsolve([ode,IC1]);
Please Wait...