Check whether solutions of the following ivp exist:
$$y''+e ^{x}y=x ^{2}$$ --- y(0)=1, y'(0)=0

Question

Check whether solutions of the following ivp exist:
$$y''+e ^{x}y=x ^{2}$$  --- y(0)=1, y'(0)=0

amistre64 · Answer

is there a certain chk to perform, or is the intent to solve the diffyQ and check?

anonymous · Answer

I'm not sure. The problem says no to solve the equation. Do you plug in the initial conditions? But if so you don't have a y''.

amistre64 · Answer

then theres some thrm or another that relates to this from your related text

amistre64 · Answer

a wronskian is about all i can think of at the moment, but im sure that wouldnt be applicable

anonymous · Answer

Is there someway to check without actually solving the problem?

amistre64 · Answer

im sure there is, which would relate to some thrm or another from the text that goes along with the material. Im just not too sure what that thrm might be http://www.wolframalpha.com/input/?i=y%E2%80%B2%E2%80%B2%2Be%5Ex+y%3Dx%5E2

amistre64 · Answer

amistre64 · Answer

seems that taking the df/dy of the y'' rewrite might be helpful

anonymous · Answer

What do you mean? y'' doesn't have a variable in front

amistre64 · Answer

y′′ = x^2 - e^x y

df/dy = -e^x

amistre64 · Answer

since this is continuous at all y values, and all x values ...

anonymous · Answer

I believe that would only apply if the equation was non linear

amistre64 · Answer

without any thrms from your text that relates to this, it was a shot in the dark :)

amistre64 · Answer

good luck tho

anonymous · Answer

Thanks, I'll see if I can find something