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A homogeneous differential equation of the form M(x, y) dx + N(x, y) dy = 0 can be reduced to a differential equation with separated variables by using the substitution?

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A homogeneous differential equation of the form M(x, y) dx + N(x, y) dy = 0 can be reduced to a differential equation with separated variables by using the substitution? Answer: y = vx, dy = vdx + xdv

To solve a homogeneous differential equation of the form \(M(x,y)dx+N(x,y)dy=0\), you use the substitution \(y=vx\), along with its differential \(dy=vdx+xdv\).

Question context

This question is part of ⚡ Electrical Engineering within the broader 🛠️ Engineering Essentials subject and appears in the SPSC – Sindh Public Service Commission preparation collection. Reviewing the answer together with nearby questions helps reinforce the underlying concept and identify how it may appear in competitive exams.