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I have a problem, problem is desolve
i write desolve(x*y''+(x-1)*y'-y=x^2,y) on the g2 but its cannot this , i get warning polynomial solution found x-1 and
i get anwser
y=(x-1)*((-G_0*e^(-x)+x^2-x+1)/(x-1)+G_1) but this is not true.
True is the y=(x^2+(c1-2)*x)+2-c1+c2*e^(-x)
If you use expand, and then collect, to rewrite the Prime's solution you'll see it is basically the same expression.
I didn't find same solution i tried to your solve but didnt work
Let me be a bit more clear. I press CAS first, entering in textbook mode (which I show here as algebraic, directly copied and pasted from the virtual calculator).
If you give desolve(x*y''+(x-1)*y'-y=x^2,y), you get as result (x-1)*((-G_0*e^(-x)+x^2-x+1)/(x-1)+G_1)
If you enter expand(Ans), you get G_1*x+x^3/(x-1)-2*x^2/(x-1)+2*x/(x-1)+G_0*e^(-x)/(x-1)-G_0*x*e^(-x)/(x-1)-G_1-1/(x-1) which doesn't look like progress yet.
Now enter collect(Ans) to get -G_0*e^(-x)+G_1*x+x^2-G_1-x+1 and this effectively the solution you gave.
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