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Homogeneous Differential Equation


Definition

A homogeneous differential equation is one that can we written in the following form: $\frac{dy}{dx}=F\left(\frac{y}{x}\right)$.

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Problems Solved

$\frac{dy}{dx}=-\frac{4x+3y}{2x+y}$
$\frac{dy}{dx}=\frac{\left(x^2+2y^{2\:}\right)}{xy}$
$\left(x+2y\right)dx\:+\left(y\right)dy\:=0$
$\frac{dy}{dx}=\left(\frac{2x-y}{x+4y}\right)$
$\left(y^2+2\cdot\:\:x\cdot\:\:y\right)\cdot\:\:dx-x^2\cdot\:\:dy$
$\frac{dy}{dx}=\frac{3x^2+4y^2}{xy}$
$\frac{dy}{dx}=\frac{\left(2x^2-2xy+y^2\right)}{x^2}$

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