JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

y=(A+B x) e^{m x}+(m-1)^{-2} e^x

, then

\frac{d^2 y}{d x^2}-2 m \frac{d y}{d x}+m^2 y

is equal to

View answer and explanation

Correct option: A

e^x

Option A (

e^x

) is correct because substituting the given

y

into the differential equation results in

e^x

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y=y(x)

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x

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

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

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

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y=y_{2}(x)

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

y_{1}(0)=0

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y=y_{1}(x)

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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)