The general solution of the differential equation `(dy)/(dx)+(2)/(x)y=x^(2)`, is

Options

A. `y=cx^(2)+(x^(3))/(5)`
B. `y=cx^(-2)+(x^(3))/(5)`
C. `y=cx^(3)-(x^(3))/(4)`
D. `y=cx^(-3)(x^(2))/(4)`

Answer

B

Explanation

The general solution of the differential equation `(dy)/(dx)+Py=Q`, where `P=(2)/(x) and Q=x^(2)`.
I.E. `=e^(intPdx)=e^(int(2)/(x)dx)=e^(2logx)+x^(2)`
Multiplying both sides of the differential equation by I.E. `=x^(2)` and integrating with respect to x, we get
`yx^(2)=(x^(5))/(5)+c or, y=(x^(3))/(5)+cx^(-2)`