Mathematics · important
Alternative derivation of linear homogeneous first-order DE for JEE
Solution of a homogeneous and linear differential equation of the type dy/dx + p(x)y = q(x)
Formula
\(\dfrac{dy}{dx}=-p(x)y\Rightarrow \dfrac{dy}{y}=-p(x)dx\Rightarrow \log|y|=-\int p(x)dx + C\)
Variables: \(p(x)\) is a function of \(x\).
Conditions: Valid for \(y\neq 0\) during separation; \(y=0\) also satisfies the equation.
Quick solution of the homogeneous linear case by separation.