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Question: why DEtools:-particularsol hangs when dsolve works?

Question:why DEtools:-particularsol hangs when dsolve works?

nm 8552 Maple 2020
ode detools differential-equations
October 21 2020
1

I solved this linear constant coefficients ode by hand, and wanted to use Maple to check my solution.

dsolve works with no problem. I wanted to check the particular solution on its own, so called DEtools:-particularsol(ode,y(x)); but was surprised it hangs.

Why would DEtools:-particularsol(ode,y(x)); hang, when dsolve gives the complete solution (including particular solutin ofcourse) right away?  It is 7th order ODE. But nothing special. Linear and constant coefficients. Since dsolve solves it right away, I expected DEtools:-particularsol to have no problem as well.

restart;
ode:=diff(y(x),x$7)-2*diff(y(x),x$6)+9*diff(y(x),x$5)-16*diff(y(x),x$4)+24*diff(y(x),x$3)-32*diff(y(x),x$2)+16*diff(y(x),x)=exp(2*x)+x*sin(x)+x^2;

dsolve(ode);  #no problem.

#this hangs. Why?
DEtools:-particularsol(ode,y(x));


 

> 

interface(version);

`Standard Worksheet Interface, Maple 2020.1, Windows 10, July 30 2020 Build ID 1482634`

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 851. The version installed in this computer is 847 created 2020, October 17, 17:3 hours Pacific Time, found in the directory C:\Users\me\maple\toolbox\2020\Physics Updates\lib\`

> 

restart;
ode:=diff(y(x),x$7)-2*diff(y(x),x$6)+9*diff(y(x),x$5)-16*diff(y(x),x$4)+24*diff(y(x),x$3)-32*diff(y(x),x$2)+16*diff(y(x),x)=exp(2*x)+x*sin(x)+x^2;

diff(diff(diff(diff(diff(diff(diff(y(x), x), x), x), x), x), x), x)-2*(diff(diff(diff(diff(diff(diff(y(x), x), x), x), x), x), x))+9*(diff(diff(diff(diff(diff(y(x), x), x), x), x), x))-16*(diff(diff(diff(diff(y(x), x), x), x), x))+24*(diff(diff(diff(y(x), x), x), x))-32*(diff(diff(y(x), x), x))+16*(diff(y(x), x)) = exp(2*x)+x*sin(x)+x^2

> 

#this works
sol:=dsolve(ode)

y(x) = (5/16)*x+(1/128)*exp(2*x)+(1/8)*x^2-(1/4)*exp(-(2*I)*x)*_C3-(1/4)*exp((2*I)*x)*_C3-exp(x)*_C4+(1/8)*exp(-(2*I)*x)*_C5+(1/8)*exp((2*I)*x)*_C5+((1/36)*I)*exp(-I*x)-((1/36)*I)*exp(I*x)-((67/57600)*I)*exp(-(2*I)*x)+((67/57600)*I)*exp((2*I)*x)+((1/4)*I)*exp(-(2*I)*x)*_C5*x-((1/4)*I)*exp((2*I)*x)*_C5*x+(67/28800)*x*exp((2*I)*x)+(67/28800)*x*exp(-(2*I)*x)-(1/4)*exp(-(2*I)*x)*_C6*x-(1/4)*exp((2*I)*x)*_C6*x-((1/36)*I)*exp(I*x)*x+((1/36)*I)*exp(-I*x)*x+((67/21600)*I)*exp(-(2*I)*x)*x+((1/4)*I)*exp(-(2*I)*x)*_C2+((1/8)*I)*exp(-(2*I)*x)*_C6-((67/21600)*I)*exp((2*I)*x)*x-((1/4)*I)*exp((2*I)*x)*_C2-((1/8)*I)*exp((2*I)*x)*_C6+(67/43200)*exp((2*I)*x)+(67/43200)*exp(-(2*I)*x)+(1/54)*exp(-I*x)+(1/54)*exp(I*x)+_C4*exp(x)*x+(1/48)*x^3+_C7+_C1*exp(x)

> 

#this hangs. Why?
DEtools:-particularsol(ode,y(x));
> 

 


 

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