find the general solution of
dz/dt=5ze^(sint)cost+2e^(sint)cost

The general solution of given differential equation is .

Step-by-step explanation:

The given differential equation is

Taking out common factors.

Using variable separable method, we get

Integrate both sides.

        .... (1)

First solve LHS,

Substitute

Now, solve RHS,

Substitute ,

Subtitle the values of I₁ and I₂ in equation (1).

Therefore the general solution of given differential equation is .