Solve `x(dy)/(dx) +2y = x^2logx`

Answer

` y=(x log x)/(4)-x/3+c`

Explanation

We have,


`x (dy)/(dx)+2 y=x^2 log x `


`(dy)/(dx)+2 y/x=(x^2 log x)/x `


`(dy)/(dx)+2 y/x=x log x`


Comparing this equation


`(dy)/(dx)+Py=Q`


Then, `P=2/x, quad Q=x log x`


`I.F.=e^(int P dx) `


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