JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Hard

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Analyzing +4 | -1

y=(1+x)\left(x^{2}+1\right)\left(x^{4}+1\right)\left(x^{8}+1\right)\left(x^{16}+1\right)

, then find the value of

y^{\prime \prime}-y^{\prime}

x=-1

View answer and explanation

Correct option: C

-496

Option C (-496) is correct because after simplifying the expression for y and differentiating twice, substituting x = -1 yields y'' - y' = -496.

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

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

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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)