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Provide solution for  RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 45 textbook solution.

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Answer : \text { (b) } \frac{d^{2} y}{d x^{2}}-y=0

Hint : Differentiate the equation twice with respect to x

Given :    y=C_{1} e^{x}+C_{2} e^{-x}                          ....(ii)

Explanation :  Differentiate on both sides with respect to x

\Rightarrow \frac{d y}{d x}=C_{1} e^{x}-C_{2} e^{-x}

Again, differentiate with respect to x

\begin{aligned} &\Rightarrow \frac{d^{2} y}{d x^{2}}=C_{1} e^{x}+C_{2} e^{-x}\\ &\Rightarrow \frac{d^{2} y}{d x^{2}}=y \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \quad[\text { from }(i)] \end{aligned}

\Rightarrow \frac{d^{2} y}{d x^{2}}-y=0

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