GATE 2022 PI – Question 37

Engineering Mathematics · Differential Equations · 2 marks · Multiple choice

Find the general solution of $4y^{\prime\prime}-4y^\prime+y=0$, with arbitrary constants c₁,c₂.

$y=(c_1+c_2x)e^x$
$y=c_1e^{x/2}+c_2e^x$
$y=c_1e^x+c_2e^{2x}$
$y=(c_1+c_2x)e^{x/2}$

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Show answer and explanation

Correct answer: (D) $y=(c_1+c_2x)e^{x/2}$

Explanation

The characteristic equation is $4m^2-4m+1=(2m-1)^2=0$, a repeated root m = 1/2. Two independent solutions are e^(x/2) and xe^(x/2), giving **D**.

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