If y = A x e ∫ P d x is a solution of d y d x + P x y = Q x , then A ' ( x ) =

Step-by-step solution

The solution is given as, y = A x e ∫ P d x The above equation is a linear differential equation. The integral factor is, IF = e ∫ P ( x ) d x The solution is, y ( IF ) = ∫ Q ( x ) × IF d x y e ∫ P ( x ) d x = ∫ Q x e ∫ P ( x ) d x d x Substitute the values in the above equation from given expression. A x = ∫ Q x e ∫ P ( x ) d x d x ⇒ A ' x = Q x e ∫ P ( x ) d x