✓ Board-verified
Mathematics · 2026 · 1 mark
Differential EquationsMethods of Solving First Order, First Degree Differential Equations1 markUnderstandmcq
CBSE 2026 · Region 3 · Set 1 · Q13
(d y)/(d x)= F ( x, y ) will be a homogeneous differential equation for which of the following functions? (i) F ( x, y )=3 x +2 y (ii) F ( x, y )=…
$\displaystyle \frac{d \mathrm{y}}{d \mathrm{x}}=\mathrm{F}(\mathrm{x}, \mathrm{y})$ 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)
$\displaystyle \mathrm{F}(\mathrm{x}, \mathrm{y})=\sqrt{\mathrm{x}^{2}+\mathrm{y}^{2}}-\mathrm{y}$
Official answer
(D)
(ii) and (iii)
All Differential Equations questions2026 question paperNCERT solutions: Differential EquationsPractice Differential Equations →
More from Differential Equations
- The integrating factor of the differential equation (1-y^2) (d x)/dy+y x=ay,(-1<y<1) is2023
- The integrating factor for solving the differential equation x dy/dx-y=2 x^2 is:2023
- Product of the order and degree of differential equation 1+(dy/dx)^3=λ((d^3 y)/(dx^3))^2 is:2026
- Solve the differential equation (d y)/(d x)= cos x-2 y.2025
- The solution of the differential equation (d x)/x+(d y)/y=0 is:2023
- Find the general solution of the differential equation (y^2-x^2) d x=2 x y dy OR Find the particular solution of the differential equation (1+e^2 x)…2026
- The integrating factor of the differential equation (x+2 y^2) (d y)/(d x)=y(y>0) is:2024
- Find the particular solution of the differential equation dy/dx-y/x+cosec(y/x)=0; given that y=0, when x=1.2025
CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.