Find the equation of a curve passing through the point (0, 0) and whose differential equation is `y^(prime)=e^xsinx`

Answer

`y=1/2[e^x(sin x-cos x)+1]`

Explanation

We are given the differential equation


`yprime=e^xsinx`


`rArr (dy)/(dx)=e^xsinx`


`rArr dy=e^xsinxdx`


Integrating both sides,


`int dy=int e^xsinxdx`


`rArr y=int e^xsinxdx---(1)`


Let, `int e^x sin x d x=I`


...