## anonymous one year ago 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.

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1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

I think I'm struggling with what happens after that

5. amistre64

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

6. amistre64

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

7. amistre64

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

8. anonymous

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...

9. amistre64

good luck