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  • Provide solution for RD Sharma class 12 chapter 21 Diffrential Equations excercise 21.4 question 4

Provide solution for RD Sharma class 12 chapter 21 Diffrential Equations  excercise 21.4 question 4

Answers (1)

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Answer:   y=e^{x}+1  is the solution of given function

 Hint:

Take the differentiation of the function y=e^{x}+1

Given:                      

     y=e^{x}+1  is the function.

Solution:                              

Differentiating with respect to  x

\Rightarrow \frac{d y}{d x}=e^{x} \cdots(i)

Again differentiating eq(i)

\begin{aligned} &\Rightarrow \frac{d^{2} y}{d x^{2}}=e^{x} \\ &\Rightarrow \frac{d^{2} y}{d x^{2}}=\frac{d y}{d x} \quad\left[\because \frac{d y}{d x}=e^{x}\right] \\ &\Rightarrow \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0 \end{aligned}

Thus,  y=e^{x}+1 satisfies the function.

Now,

When    x=0

              \begin{aligned} y &=e^{0}+1 \\ &=1+1 \\ &=2 \end{aligned}

Now,

When    x=0

y^{\prime}=e^{x}=e^{0}=1

Thus both  y(0)=2 \text { and } y^{\prime}(0)=1 satisfies the initial value  problem

 

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