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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 2 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise  Revision Exercise Question 2 Maths Textbook Solution.

Answers (1)

Answer:

                Verified

Hint:

Find double derivatives of given equation and put values to verify

Given:

            y=e^{-3x}

Prove that y=e^{-3x}  is the solution of \frac{d^{2}y}{dx^{2}}+\frac{dy}{dx}-6y=0

Solution:

                y=e^{-3x}

                \begin{aligned} &\frac{d y}{d x}=-3 e^{-3 x} \\ &\frac{d^{2} y}{d x^{2}}=(-3)(-3) e^{-3 x} \\ &\frac{d^{2} y}{d x^{2}}=9 e^{-3 x} \end{aligned}

Put it in equation

                        \begin{aligned} &\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}-6 y=0 \\ &9 e^{-3 x}-3 e^{-3 x}-6 e^{-3 x}=0 \\ &\Rightarrow 0 \end{aligned}

Hence proved.

 

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infoexpert21

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