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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.
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ dy }{ dx }=e^yx^2\] Start by getting the x's and y's on different sides of the equation. Is it integrating you had trouble with?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits e^{y}dy=\int\limits x^2dx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah 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
 one year ago
Best ResponseYou've already chosen the best response.0I think I'm struggling with what happens after that

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1e^(y) dy, integrates to e^(y)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1\[e^{y}=\frac13x^3+C\] \[e^{y}=\frac13x^3+C\] \[ln(e^{y})=ln(\frac13x^3+C)\] \[y=ln(\frac13x^3+C)\] \[y=ln(\frac13x^3+C)\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1of course there needs to be some restrictions or absolute value bars to make things proper i spose

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhh, 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...
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