Recent questions in Ordinary Differential Equation (ODE)

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If $\text{k}$ is a constant, the general solution of $\dfrac{dy}{dx}-\dfrac{y}{x}=1$ will be in the form of$y=x\text{ ln}(kx)$$y=k\text{ ln}(kx)$$y=x\text{ ln}(x)$$y=xk\t...
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The ordinary differential equation $\dfrac{d^2u}{dx^2}$$- 2x^2u +\sin x = 0$ islinear and homogeneouslinear and nonhomogeneousnonlinear and homogeneousnonlinear and nonho...
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Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round of...
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The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2-a^2} \\$$\dfrac{a}{s^2 + a^2} \\$$\dfrac{s}{s^2-a^2} \\$$\dfrac{s}{s^2+a^2}$
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The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is$Q(t)=e^{-t}-1$$Q(t)=1+ e^{-t}$$Q(t)=1 -e^t$$Q(t)=1- e^{-t}$
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The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is$e^{-k_1t} \\$$e^{-k_2t} \\$$e^{k_1t} \\$$e^{k_2t}$
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The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is$y=e^{-2x}$$y=2e^{-2x}$$y=10.95 e^{-2x}$$y=36.95 e^{...
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The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is$x$$x^2$$x^{-1}$$x^{-2}$
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