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CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Q131 Markshomogeneous_equations

CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Question 13 (Differential Equations)

For which right-hand sides is dy/dx=F(x,y) homogeneous? (i) 3x+2y, (ii) sin(y/x)+ln y−ln x, (iii) exp(y/x)+1, (iv) √(x²+y²)−y.

(A) (i) and (ii)
(B) (i), (ii) and (iii)
(C) (ii), (iii) and (iv)
(D) (ii) and (iii)

✅ Step-by-Step Solution

Final Answer: (ii) and (iii)

The homogeneous first-order form depends only on y/x. Both (ii), with ln y−ln x=ln(y/x) on its domain, and (iii) have that form.

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