Mathematics · essential
Reduction of homogeneous equation to separable form for JEE
Solution of a homogeneous and linear differential equation of the type dy/dx + p(x)y = q(x)
Formula
\(v+x\dfrac{dv}{dx}=F(v)\Rightarrow x\dfrac{dv}{dx}=F(v)-v\Rightarrow \dfrac{dv}{F(v)-v}=\dfrac{dx}{x}\)
Variables: \(v=y/x\).
Conditions: Applicable after substituting \(y=vx\) in \(\dfrac{dy}{dx}=F(y/x)\).
Main solving step for homogeneous first-order equations.