Question

`x^2 dy/dx +2x^2y= x^2 e^(-2x)` PLEASE HELP Integrating factor?

The solution i get is e^-2x + C, however this seems to be incorrect. Can anybody please help?

Answer 1

`y = e^(-2x)( x + C)`

Explanation:

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

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

With integrating factor, `Omega(x)`:

• `Omega(x) = e^(int 2 dx) = alpha e^(2x)`

`Omega(x) ( dy/dx +2 y= e^(-2x) )`

`alpha e^(2x) dy/dx +2alpha e^(2x) y= alpha e^(2x)e^(-2x)`

`e^(2x) dy/dx +2 e^(2x) y= 1`

`( e^(2x) y)^' = 1`

`e^(2x) y = x + C`

`y = e^(-2x)( x + C)`