EC > GATE 2024 > Differential Equations
The general form of the complementary function of a differential equation is given by $y(t)=(At+B)e^{-2t}$, where A and B are real constants determined by the initial condition.
The corresponding differential equation is
A
$\frac{d^{2}y}{dt^{2}}+4\frac{dy}{dt}+4y=f(t)$
B
$\frac{d^{2}y}{dt^{2}}+4y=f(t)$
C
$\frac{d^{2}y}{dt^{2}}+3\frac{dy}{dt}+2y=f(t)$
D
$\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=f(t)$

Correct : A

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differential equation complementary function GATE EC 2024 second order differential equation y(t) form initial conditions EC gate differential equation form complementary function form

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