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2xy^2dx=e^x(dy-ydx) solve the above diffrantial eqation

2xy^2dx=e^x(dy-ydx) solve the above diffrantial eqation 

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1 Answers

jagdish singh singh
173 Points
8 years ago
\hspace{-0.6 cm }$Given $\bf{2xy^2dx=e^x(dy-ydx)\Rightarrow 2xdx = \frac{e^x(dy-ydx)}{y^2}}$\\\\\\So we get $\bf{-2xdx = \frac{ye^xdx-e^xdy}{y^2} =d\left( \frac{e^x}{y}\right)\Rightarrow d\left( \frac{e^x}{y}\right)=-2xdx}$\\\\\\ So we get $\bf{\frac{e^x}{y}=-x^2+\mathcal{C} \Rightarrow y=\frac{e^x}{-x^2+\mathcal{C}}.}$

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