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Number 4. Find the general solution of each differential equation

Number 4. Find the general solution of each differential equation-example-1

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To solve the given differential equation, proceed as follows:


\begin{gathered} (dy)/(dx)=(2x)/(e^(2y)) \\ e^(2y)dy=2xdx \end{gathered}

Use integrals to solve for y and x:


\begin{gathered} \int e^(2y)dy=\int 2xdx \\ (e^(2y))/(2)=x^2+C \end{gathered}

Solve for y:


\begin{gathered} e^(2y)=2x^2+C \\ 2y=\ln |2x^2+C| \\ y=(\ln |2x^2+C|)/(2) \end{gathered}

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