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Maths-

General

Easy

Question

Solution of differential equation $fraction numerator d y over denominator d x end fraction plus a y equals e to the power of m x end exponent$ is

$(a + m) y = e^{m x} + c$
$y e^{a x} = m e^{m x} + c$
$y = e^{m x} + c e^{- a x}$
$(a + m) y = e^{m x} + c e^{- a x}$

hint Hint:

In this question we have to find the solution of the differential equation. For this we will find the IF and then the solution.

The correct answer is: $left parenthesis a plus m right parenthesis y equals e to the power of m x end exponent plus c e to the power of negative a x end exponent$

$fraction numerator d y over denominator d x end fraction plus a y equals e to the power of m x end exponent I n t e g r a t i n space f a c t o r equals e to the power of integral P d x end exponent equals e to the power of integral a space d x space end exponent equals e to the power of a x end exponent y open parentheses e to the power of a x end exponent close parentheses equals integral e to the power of a x end exponent. e to the power of m x end exponent space. d x plus C space space space space space space space space space space space equals integral e to the power of open parentheses a plus m close parentheses x end exponent d x plus C space space space space space space space space space space space equals fraction numerator e to the power of open parentheses a plus m close parentheses x end exponent over denominator a plus m end fraction plus C rightwards double arrow open parentheses a plus m close parentheses y equals fraction numerator e to the power of a x end exponent. e to the power of m x end exponent over denominator e to the power of a x end exponent end fraction plus C over e to the power of a x end exponent rightwards double arrow open parentheses a plus m close parentheses y equals e to the power of m x end exponent plus C e to the power of negative a x end exponent$

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