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  • Need solution for RD Sharma maths class 12 chapter 21 Diffrential Equations exercise 21.4 question 5

 Need solution for RD Sharma maths class 12 chapter 21 Diffrential Equations  exercise 21.4 question 5

Answers (1)

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Answer: y=e^{-x}+2 is the solution of given function

Hint:

Differentiate the function and then obtain the value and satisfy initial value of problem.

Given:                      

 y=e^{-x}+2 is the function. 

Solution:                              

Differentiating on both sides with respect to  x

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

\begin{aligned} &\text { For } e^{-x}=y-2 \quad\left[\therefore y=e^{-x}+2\right] \\ &\Rightarrow \frac{d y}{d x}=-(y-2) \\ &\Rightarrow \frac{d y}{d x}=-y+2 \\ &\Rightarrow \frac{d y}{d x}+y=2 \end{aligned}

Thus,

y=e^{-x}+2 satisfies the equation

\begin{aligned} &\text { Now, When }\\ &x=0\\ &y=e^{-(0)}+2\\ &y=1+2\\ &y=3 \end{aligned}

Thus, y(0)=3 solves initial value problem

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