GATE 2026 ES – Question 36
Classify the differential equation $dy/dx+x^2y=0$.
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Correct answer: (C) Linear, homogeneous and nonexact
Explanation
The equation is linear in $y,y^{\prime}$ and has zero forcing, so it is a homogeneous linear ODE. In differential form $Mdx+Ndy=0$,where $M=x^2y,N=1$. Since $\partial M/\partial y=x^2$ differs from $\partial N/\partial x=0$,the given differential form is not exact. Therefore **C**.