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  • Need solution for RD Sharma maths class 12 chapter 21 Differential Equations exercise 21.4 question 7

 Need solution for RD Sharma maths class 12 chapter 21 Differential Equations exercise 21.4 question 7

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Answer:   y=e^{x}+e^{-x}  is the solution of given function

Hint:

Differentiate the function and then substitute

Given: 

y=e^{x}+e^{-x}  is the function.

Solution:                              

Differentiating   y=e^{x}+e^{-x} with respect to  x

\begin{aligned} &\Rightarrow \frac{d y}{d x}=e^{x}-e^{-x} \cdots(i)\\ &\text { Again differentiating eq(i) }\\ &\Rightarrow \frac{d^{2} y}{d x^{2}}=e^{x}+e^{-x}\\ &\Rightarrow \frac{d^{2} y}{d x^{2}}=y\\ &\Rightarrow \frac{d^{2} y}{d x^{2}}-y=0 \end{aligned}

Thus  y=e^{x}+e^{-x} satisfies the equation

Now, when x=0

\begin{aligned} \mathrm{y} &=\boldsymbol{e}^{0}+e^{-(0)} \\ &=1+1=2 \end{aligned}

Now, when x=0

\begin{aligned} \mathrm{y}^{\prime} &=e^{0}-e^{-(0)} \\ &=1-1=0 \end{aligned}

Thus both y(0)=2 \text { and } y^{\prime}(0)=0 satisfies the equation

 

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