Let y = y x be the solution curve of the differential equation d y d x + 2 x 2 + 11 x + 13 x 3 + 6 x 2 + 11 x + 6 y = x + 3 x + 1 , x > - 1 , which passes through the point 0 , 1 . Then y 1 is equal to

Step-by-step solution

Given, d y d x + 2 x 2 + 11 x + 13 x 3 + 6 x 2 + 11 x + 6 y = x + 3 x + 1 Now comparing with d y d x + y × p x = q x We get p x = 2 x 2 + 11 x + 13 x 3 + 6 x 2 + 11 x + 6 So I F = e ∫ 2 x 2 + 11 x + 13 x 3 + 6 x 2 + 11 x + 6 d x Now finding the integration we get, ∫ p x d x = ∫ 2 x 2 + 11 x + 13 d x x + 1 x + 2 x + 3 Using partial fraction we get, 2 x 2 + 11 x + 13 x + 1 x + 2 x + 3 = A x + 1 + B x + 2 + C x + 3 On solving we get A = 4 2 = 2 , B = 1 and C = - 1 So, ∫ p x d x = A ln x +