Given Differential Equation :

Formula :

i)

ii)

iii)

iv)

v)

vi) General solution :

For the differential equation in the form of

General solution is given by,

Where, integrating factor,

Answer :

Given differential equation is

………eq(1)

Equation (1) is of the form

Where, and

Therefore, integrating factor is

………

General solution is

………eq(2)

Let,

Let, u=sin x and v=e^2x

………

………

Again, let u=cos x and v=e^2x

………

………

Multiplying above equation by 4,

Substituting I in eq(2),

Dividing above equation by e^2x,

Therefore general equation is