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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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.

Calculus1
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\[\frac{ dy }{ dx }=e^yx^2\] Start by getting the x's and y's on different sides of the equation. Is it integrating you had trouble with?
\[\int\limits e^{-y}dy=\int\limits x^2dx\]
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

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I think I'm struggling with what happens after that
e^(-y) dy, integrates to -e^(-y)
\[-e^{-y}=\frac13x^3+C\] \[e^{-y}=-\frac13x^3+C\] \[ln(e^{-y})=ln(-\frac13x^3+C)\] \[-y=ln(-\frac13x^3+C)\] \[y=-ln(-\frac13x^3+C)\]
of course there needs to be some restrictions or absolute value bars to make things proper i spose
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...
good luck

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