KCET2020MathematicsVector Algebra
The general solution of the differential equation x² d y-2 x y d x=x⁴ x d x is
Options
- Ay=x² x+c x²
- By=x² x+c
- Cy= x+c x²
- Dy= x+c x²
Correct answer
A. y=x² x+c x²
Step-by-step solution
We have, aligned x² d y-2 x y d x &=x⁴ x d x d y d x - 2 x y &=x² x aligned Comparing with d y d x +P y=Q Where P=- 2 x and Q=x² x IF =e^ -2 x d x =e^ -2 x =e^ ( 1 x² ) = 1 x² The solution of the given differential y IF = (Q IF ) d x+c y 1 x² = (x² x ) ( 1 x² ) d x+c y x² = x+c y x² = x+c y=x² x+c x²