99 Percentile Qs Bank for JEE MainMathematicsDifferential Equations
Solution of differential equation x 2 y − x 3 dy dx = y 4 cosx is :
Options
- Ax 2 y − 3 = 2 sin x + c
- Bx 2 y − 3 = 3 cos x + c
- Cx 3 y − 3 = 3 sin x + c
- Dx 2 y 3 = 3 sin x + c x 2 y
Correct answer
C. x 3 y − 3 = 3 sin x + c
Step-by-step solution
x 2 y − x 3 d y d x = y 4 cos x 1 y 4 d y d x + ( − 1 x ) 1 y 3 = cos x 3 put 1 y 3 = v 1 y 4 d y d x = − 1 3 d v d x − 1 3 d v d x + ( − − 1 x ) v = − cos x x 3 d v d x + 3 x v = 3 cos x I.F.= e 3 ∫ 1 x d x = x 3 solution v . x 3 = 3 ∫ cos x d x + c 1 y 3 x 3 = 3 sin x + c x 3 y − 3 = 3 sin x + c .