Mathematics · important
Equivalent homogeneous differential form for JEE
Solution of a homogeneous and linear differential equation of the type dy/dx + p(x)y = q(x)
Formula
\(M(x,y)\,dx+N(x,y)\,dy=0\) with \(M,N\) homogeneous functions of the same degree
Variables: \(M\) and \(N\) satisfy \(M(tx,ty)=t^nM(x,y)\), \(N(tx,ty)=t^nN(x,y)\).
Conditions: Both functions must be homogeneous of the same degree.
Checking whether a DE is homogeneous before substitution.