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GATE2018-2-4

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The Laplace transform of $e^{i5t}$ where $i=\sqrt{-1}$, is$\dfrac{s-5i}{s^2-25} \\$$\dfrac{s+5i}{s^2+25} \\$$\dfrac{s+5i}{s^2-25} \\$$\dfrac{s-5i}{s^2+25} $
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Given the ordinary differential equation $$\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}-6y=0$$ with $y(0)=0$ and $\dfrac{dy}{dx}(0)=1$, the value of $y(1)$ is __________ (correct to...
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The solution of $$\dfrac{d^2y}{dt^2}-y=1,$$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is$\dfrac{1}...
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The Laplace transform of $e^{i5t}$ where $i=\sqrt{-1}$, is$\dfrac{s-5i}{s^2-25} \\$$\dfrac{s+5i}{s^2+25} \\$$\dfrac{s+5i}{s^2-25} \\$$\dfrac{s-5i}{s^2+25} $
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