CBSE Class 12 Mathematics 2026: question 28

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Rewrite as a linear equation in $x$: $\frac{dx}{dy}=\frac{x+2y^3}{y}$, i.e. $\frac{dx}{dy}-\frac{x}{y}=2y^2$. Here $P=-\frac{1}{y}$ and $Q=2y^2$.

   ½ mark

2. I.F. $=e^{\int -\frac{1}{y}dy}=e^{-\log y}=\frac{1}{y}$ (taking $y>0$)

   1 mark

3. The solution is $x\cdot \frac{1}{y}=\int 2y^2\cdot \frac{1}{y}dy+C=\int 2ydy+C$

   1 mark

4. $\frac{x}{y}=y^2+C$, i.e. $x=y^3+Cy$

   ½ mark

Answer: $x=y^3+Cy$ (or $\frac{x}{y}=y^2+C$)

Revise the chapter

• Chapter: Differential Equations (notes, formulas, where marks are lost and every past question)
• Topic: Linear Differential Equations