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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)

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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