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  • Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.3 question 20 maths

Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.3 question 20 maths

Answers (1)

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Answer:

y=e^{-x}+a x+b  is a solution of differential equation

Hint:

Just differentiate two times to obtain values.

Given:

y=e^{-x}+a x+b

Solution:

y=e^{-x}+a x+b

Differentiating on both sides with respect to x

\begin{aligned} &\Rightarrow \frac{d y}{d x}=\frac{d}{d x}\left(e^{-x}+a x+b\right) \\\\ &\Rightarrow \frac{d y}{d x}=-e^{-x}+a \end{aligned}            ................(i)

Differentiating equation (i)

\begin{aligned} &\Rightarrow \frac{d^{2} y}{d x^{2}}=-\left(-e^{-x}\right) \\\\ &\Rightarrow \frac{d^{2} y}{d x^{2}}=\left(e^{-x}\right) \\\\ &\Rightarrow e^{x} \cdot \frac{d^{2} y}{d x^{2}}=1 \end{aligned}

Thus, \Rightarrow y=e^{-x}+a x+b is a solution.

 

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