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Homogeneous Differential Equation


Definition

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


Problems Solved

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

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