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Provide solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 7 textbook solution.

Answers (1)

Answer : (c) y^{\prime \prime}=-w^{2} y

Hint: Differentiate the differential equation with respect to t.

Given:  y=A \cos w t+B \sin w t                                 ...(i)

Explanation :

\begin{aligned} &\frac{d y}{d x}=-A \sin w t w+B \cos w t w \\ &=-A w \sin w t+B w \cos w t \end{aligned}

\begin{aligned} &\frac{d^{2} y}{d x^{2}}=-A w \cos w t(w)-B w \cos w t(w) \\ &\frac{d^{2} y}{d x^{2}}=-w^{2}(A \cos w t+B w \cos w t) \end{aligned}

From (i)

\begin{aligned} &\frac{d^{2} y}{d x^{2}}=-w^{2} y \\ &y^{\prime \prime}=-w^{2} y \end{aligned}

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