The solution of the equation  \frac{d^{2}y}{dx^{2}}=e^{-2x}

  • Option 1)

    \frac{1}{4}e^{-2x}\;

  • Option 2)

    \; \frac{1}{4}e^{-2x}+cx+d\;

  • Option 3)

    \; \; \frac{1}{4}e^{-2x}+cx^{2}+d\;

  • Option 4)

    \; \; \frac{1}{4}e^{-2x}+c+d\;

 

Answers (1)
V Vakul

As we learnt in 

Solution of differential equations -

A function y =f(x) is a solution of differential equation, if the substitution of f(x) and its derivative (s) in differential equation reduces it to an identity.

-

 

\frac{d^{2}y}{dx^{2}}=e^{-2x}

\frac{dy}{dx}=\frac{e^{-2x}}{-2}+C

\int dy = -\frac{1}{2}\:\int e^{-2x}dx+cx+d

y=\frac{1}{4}\:e^{-2x}\:+cx+d


Option 1)

\frac{1}{4}e^{-2x}\;

This option is incorrect.

Option 2)

\; \frac{1}{4}e^{-2x}+cx+d\;

This option is correct.

Option 3)

\; \; \frac{1}{4}e^{-2x}+cx^{2}+d\;

This option is incorrect.

Option 4)

\; \; \frac{1}{4}e^{-2x}+c+d\;

This option is incorrect.

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Knockout JEE Main January 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions