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CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Q111 Marksseparation

CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Question 11 (Differential Equations)

Choose the general nonzero solution family for \(\frac{dy}{dx}=\frac{\sqrt y}{\sqrt x}\).

(A) ln √y=ln √x+C
(B) √y+√x=C
(C) √y−√x=C
(D) ln √y+ln √x=C

✅ Step-by-Step Solution

Final Answer: √y−√x=C

On a positive branch, integrate dy/√y=dx/√x to obtain √y−√x=C. The identically zero solution also satisfies the original equation for x>0.

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