Find the solution of the differential equation \[\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{x^2 + y^2}{

Question

Find the solution of the differential equation $$\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{x^2 + y^2}{xy}$$ $$(x + y) \frac{\mathrm{d}y}{\mathrm{d}x} = x - y$$ $$x(x + y) \frac{\mathrm{d}y}{\mathrm{d}x} + y(3x + y) = 0$$

Accepted Answer

(a) $y^2 = x^2 (\ln x^2 + A)$ ; (b) $x^2 - 2xy - y^2 = A$; (c) $2x^2 y^2 + 4x^3 y = A$.

Homogeneous equations

Homogeneous equations