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anonymous
 4 years ago
Solve separable differential equation: <see attached>
anonymous
 4 years ago
Solve separable differential equation: <see attached>

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You have that \[\frac{dy}{dx}=xy^2xy^2+1=x(y^21)(y^21)=(x1)(y^21)\] \[\frac{dy}{y^21}=(x1)dx\] Using partial fractions you can rewrite the left hand side as \[\frac12\left(\frac{1}{y1}\frac{1}{y+1}\right)dy=(x1)dx\] Integrating both sides then gives \[\frac12(\lny1\lny+1)=\frac12x^2x+C\] Multiplying both sides by 2 and combining the logs gives \[\ln\left\frac{y1}{y+1}\right=\ln\left1\frac{2}{y+1}\right=x^22x+C\] Exponentiating each side gives \[1\frac{2}{y+1}=Ae^{x^22x}\] And then simplifying gives yours final answer of \[y=\frac{2}{1Ae^{x^22x}}1\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay, I got stuck at the very first line with the factoring. Thank you so much.
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