Given the differential equation dy/dx= (e^y)(x^2) and the initial condition y(1)=0, find the solution y explicitly using separation of variables.

Question

anonymous · Answer

$$\frac{ dy }{ dx }=e^yx^2$$
Start by getting the x's and y's on different sides of the equation.
Is it integrating you had trouble with?

anonymous · Answer

$$\int\limits e^{-y}dy=\int\limits x^2dx$$

anonymous · Answer

Yeah I'm struggling with the intergration part... 
I got $$(\ln e^y)/y = (1/3)x^3 + C$$

I'm not sure if I can cancel ln and e

anonymous · Answer

I think I'm struggling with what happens after that

amistre64 · Answer

e^(-y) dy, integrates to -e^(-y)

amistre64 · Answer

$$-e^{-y}=\frac13x^3+C$$
$$e^{-y}=-\frac13x^3+C$$
$$ln(e^{-y})=ln(-\frac13x^3+C)$$
$$-y=ln(-\frac13x^3+C)$$
$$y=-ln(-\frac13x^3+C)$$

amistre64 · Answer

of course there needs to be some restrictions or absolute value bars to make things proper i spose

anonymous · Answer

Ohhh, I see my mistake. After that, I just need to plug in my initial condition and find C. 
Thank you very much!!!! :) I understand why I got it wrong...

amistre64 · Answer

good luck