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

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

Answers (1)

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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