✓ Board-verified
Mathematics · 2026 · 3 marks
Differential EquationsMethods of Solving First Order, First Degree Differential Equations3 marksApplyshort answer
CBSE 2026 · Region 5 · Set 2 · Q28
Solve the differential equation y dx +( x - y^3) dy =0.
Solve the differential equation $\displaystyle \mathrm{y} \mathrm{dx}+\left(\mathrm{x}-\mathrm{y}^{3}\right) \mathrm{dy}=0$.
Marking-scheme solution
Given differential equation can be written as $\displaystyle \dfrac{dx}{dy}+\dfrac{x}{y}=y^{2}$
Integrating factor $\displaystyle =\mathrm{e}^{\int \frac{1}{y} dy}=\mathrm{e}^{\log y}=y$
Solution is $\displaystyle x \cdot y=\int y^{3} dy+C$
i.e., $\displaystyle x \cdot y=\dfrac{y^{4}}{4}+C$ or $\displaystyle x=\dfrac{y^{3}}{4}+\dfrac{C}{y}$
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.