Find the general solution of the differential equations:`(dy)/(dx)+y/x=x^2`

Options

A. `xy=(x^(4))/(4)+c`
B. `xy=x^(4)+c`
C. `xy=(x^(2))/(2)+c`
D. none of these

Answer

A

Explanation

`(dy)/(dx)+(y)/(x)=x^(2)`
Here, `P=(1)/(x)`, `Q=x^(2)`
`I.F.=e^(intPdx)=e^(int(1)/(x)dx)=e^(logx)=x`
and general solution :
`y(x)=intx^(2)(x)dx+c`
`=intx^(3)dx+c`
`impliesxy=(x^(4))/(4)+c`