CBSE Class 12 Mathematics 2026: question 22(b)

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. $\frac{dy}{dx}=-Pu\sin ux+Qu\cos ux$

   ½ mark

2. $\frac{d^{2}y}{d{x}^2}=-P{u}^2\cos ux-Q{u}^2\sin ux$

   ½ mark

3. $\frac{d^{2}y}{d{x}^2}=-u^2(P\cos ux+Q\sin ux)=-u^{2}y$

   ½ mark

4. Therefore $\frac{d^{2}y}{d{x}^2}+u^{2}y=0$. Hence proved.

   ½ mark

Answer: $\frac{d^{2}y}{d{x}^2}=-u^{2}y$, so $\frac{d^{2}y}{d{x}^2}+u^{2}y=0$ (proved)

Revise the chapter

• Chapter: Continuity and Differentiability (notes, formulas, where marks are lost and every past question)
• Topic: Parametric and Second Order Derivatives