Find the equation of a curve passing through the point (0, 0) and whose differential equation is y′ = e^{x} sin x

To find the equation of a curve that passes through point(0,0) and has differential equation

So, we need to find the general solution of the given differential equation and the put the given point in to find the value of constant.

Separating variables,

Integrating both sides,

{Using the formula, )

Now let

integrating for .

Or,

Or,

Now we are given that the curve passes through point(0,0)

Putting the value of C in ii)

So,

So the required equations become,

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