Question

Number 4. Find the general solution of each differential equation

Answer 1

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}`