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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

$x\cdot\frac{dy}{dx}+1=x+y$
$\frac{dy}{dx}=\frac{\left(3x+y\right)}{x}$
$x\left(ln\left(x\right)-ln\left(y\right)\right)dy=-y\:dx\:$
$\frac{dz}{dx}=\frac{x+z}{x}$
$\left(x^2+y^2\right)dx=\left(2xy\right)dy$
$\left(x+y\right)\frac{dy}{dx}=\left(x-y\right)$
$\left(7x+2y\right)\frac{dy}{dx}=-2x-7y$

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