Question

Solve the differential equation dy/dx+4xy=x

Answer 1

`(\mathrm dy)/(\mathrm dx)+4xy=x`

`(\mathrm dy)/(\mathrm dx)=x(1-4y)`

This ODE is separable, so you can write


`(\mathrm dy)/(1-4y)=x\,\mathrm dx`

Integrating both sides gives


`-\frac14\ln|1-4y|=\frac12x^2+C`

`\ln|1-4y|=-2x^2+C`

`1-4y=e^(-2x^2+C)`

`1-4y=Ce^(-2x^2)`

`y=\frac{1-Ce^(-2x^2)}4`