Question

Solve the following de y’=(x^2+1)y

Answer 1

Rearrange:

y'-y(x²+1)=0.

Multiply by an integrating factor. First work out ∫-(x²+1)dx=-x³/3-x.

Integrating factor=e^-x³/3-x.

We get d(ye^-(x³/3+x))/dx=0,

ye^-(x³/3+x)=C where C is the integration constant.

y=Ce^x³/3+x.