CBSE 2026 · Region 3 · Set 1 · Q13 · 1 mark

$\displaystyle \frac{d \mathrm{y}}{d \mathrm{x}}=\mathrm{F}(\mathrm{x}, \mathrm{y})$ will be a homogeneous differential equation for which of the following functions?

(i)

$\displaystyle \mathrm{F}(\mathrm{x}, \mathrm{y})=3 \mathrm{x}+2 \mathrm{y}$

(ii)

$\displaystyle \mathrm{F}(\mathrm{x}, \mathrm{y})=\sin \frac{\mathrm{y}}{\mathrm{x}}+\log \mathrm{y}-\log \mathrm{x}$

(iii)

$\displaystyle \mathrm{F}(\mathrm{x}, \mathrm{y})=\mathrm{e}^{\mathrm{y} / \mathrm{x}}+1$

(iv)

$\displaystyle \mathrm{F}(\mathrm{x}, \mathrm{y})=\sqrt{\mathrm{x}^{2}+\mathrm{y}^{2}}-\mathrm{y}$

CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.