in Ordinary Differential Equation (ODE) recategorized by
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The solution of the second-order differential equation $\dfrac{d^{2}y}{dx^{2}}+2\dfrac{dy}{dx}+y=0$ with boundary conditions $y\left ( 0 \right )=1$ and $y\left ( 1 \right )=3$ is

  1. $e^{-x}+\left ( 3e-1 \right )xe^{-x}$

  2. $e^{-x}-\left ( 3e-1 \right )xe^{-x}$

  3. $e^{-x}+\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) -1\right ]xe^{-x}$

  4. $e^{-x}-\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) -1\right ]xe^{-x}$

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