If $ \frac{d y}{d t}+\alpha \cdot y=\gamma \cdot e^{-\beta t} $, then $\mathop {\lim }\limits_{t \to \infty } y\left( t \right)$ where $ \alpha>0, \beta>0, \gamma>0, \alpha \neq \beta $, is equal to

JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Medium

1 of 1

Application +4 | -1

\frac{d y}{d t}+\alpha \cdot y=\gamma \cdot e^{-\beta t}

, then

\lim\limits_{t \to \infty } y\left( t \right)

where

\alpha>0, \beta>0, \gamma>0, \alpha \neq \beta

, is equal to

View answer and explanation

Correct option: A

Option A (0) is correct because as t approaches infinity, the terms with negative exponents approach zero, leading to a limit of 0.

Practice All Chapter MCQs →

y=y(x)

\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0

y(1)=1

\left|(y(2))^{3}-12 y(2)\right|

x

{x^2} + {y^2} = 1

\left( {y' = \frac{{dy}}{{dx}},y'' = \frac{{{d^2}y}}{{d{x^2}}}} \right)

x = A\cos 4t + B\sin 4t,

\frac{{{d^2}x}}{{d{t^2}}}

y=y_{1}(x)

y=y_{2}(x)

\frac{d y}{d x}=y+7

y_{1}(0)=0

y_{2}(0)=1

y=y_{1}(x)

y=y_{2}(x)

y=y(t)

\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}

\alpha>0, \beta>0

\gamma>0

\lim \limits_{{x \rightarrow \infty}} y(t)