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Show that Y = E−X + Ax + B is Solution of the Differential Equation E X D 2 Y D X 2 = 1

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Question

Show that y = e−x + ax + b is solution of the differential equation\[e^x \frac{d^2 y}{d x^2} = 1\]

 

Sum
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Solution

We have,
\[y = e^{- x} + ax + b.............(1)\]
Differentiating both sides of equation (1) with respect to `x`, we have

\[\frac{dy}{dx} = - e^{- x} + a..............(2)\]

Differentiating both sides of equation (2) with respect to `x`, we have

\[\frac{d^2 y}{d x^2} = e^{- x} \]
\[ \Rightarrow e^x \frac{d^2 y}{d x^2} = 1\]

Hence, the given function is a solution of the given differential equation.

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Chapter 21: Differential Equations - Exercise 22.03 [Page 25]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 21 Differential Equations
Exercise 22.03 | Q 20 | Page 25

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