# DIIFERENTIAL EQUATION: $(x^2 + y^2) dx + x (3x^2 - 5y^2) dy = 0$

( x^2 + y^2 ) dx + x (3x^2 - 5y^2 ) dy = 0

### $(x^2 + y^2)\,dx + x(3x^2 -$(x^2 + y^2)\,dx + x(3x^2 - 5y^2)\,dy = 0$The variables are not separable The equation is not homogeneous Try:$\dfrac{dy}{dx} + \dfrac{x^2 + y^2}{x(3x^2 - 5y^2)} = 0\dfrac{dx}{dy} + \dfrac{x(3x^2 - 5y^2)}{x^2 + y^2} = 0$The equation is not linear. Try:$M = x^2 + y^2$→$\dfrac{\partial M}{\partial y} = 2yN = 3x^3 - 5xy^2$→$\dfrac{\partial N}{\partial x} = 9x^2 - 5y^2$The equation is not exact Try:$\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - (9x^2 - 5y^2)}{3x^3 - 5xy^2}\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{3x^3 - 5xy^2}$The equation does not have an integrating factor that is a function of x alone Try:$\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{M} = \dfrac{2y - (9x^2 - 5y^2)}{x^2 + y^2}\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{x^2 + y^2}\$

The equation does not have an integrating factor that is a function of y alone

Wala pa akong nakitang solution. Kung meron ka na, pease share.

### Are you sure your equation is

In reply to by Jhun Vert

Are you sure your equation is correct? And based on your answer key, there should be an initial condition because there is no constant c in your answer.