Questions without an upvoted answer in Differential equations

Consider a differential equation:\[\begin{array}{c}x^{2} \dfrac{d^{2} y}{d x^{2}}+3 x \dfrac{d y}{d x}-3 y=0 \\\left.\begin{array}{r}y=3 \\\dfrac{d y}{d x}=-5\end{array}\...

​​​​Consider the differential equation$$ \frac{d y}{d x}+\frac{y}{x}=0$$Choose the CORRECT option(s) for the solution $y$.$y=x+c ; c$ is a constant$y=\frac{c}{x} ; c$ is ...

Consider the ordinary differential equation $x^{2} \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-3 y=0$, with the boundary conditions $y(x=1)=2$ and $y(x=2)=17 / 2$. The solu...

The position $x(t)$ of a particle, at constant $\omega$, is described by the equation$$\frac{d^2 x}{d t^2}=-\omega^2 x.$$The initial conditions are $x(t=0)=1$ and $\left....

The partial differential equation $$\frac{\partial u}{\partial t} = \frac{1}{\pi^{2}} \frac{\partial ^{2} u}{\partial x^{2}}$$ where, $t \geq 0$ and $x \in [0,1]$, is sub...

The equation $\dfrac{dy}{dx} = xy^{2}+ 2y+ x- 4.5$ with the initial condition $y(x= 0) = 1$ is to be solved using a predictor-corrector approach. Use a predictor based on...

For the ordinary differential equation $$\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$$ with initial conditions $y(0)=y’(0) = y’’(0)=y’’’(0)=0$, the val...

Given $\dfrac{dy}{dx}=y-20$, and $y \mid_{x=0}=40$, the value of $y$ at $x=2$ is _________ (round off to nearest integer)

Consider the following unit step function.The Laplace transform of this function is$\dfrac{e^{-3s}}{s} \\ $$\dfrac{e^{-3s}}{s^2} \\$$\dfrac{e^{-3s}}{3s} \\$$\dfrac{e^{-6s...

The solution of the ordinary differential equation$\frac{dy}{dx}+3y=1$, subjects to the initial condition $y=1$ at $x=0$, is$\frac{1}{3}\left ( 1+2e^{-x/3} \right )$$\fra...

For the initial value problem$$\frac{dx}{dt}=\sin\left ( t \right ),\:\:\:\:x\left ( 0 \right )=0$$the value of $x$ at $t=\pi /3$ , is _____________.

The Laplace transform of a function is $\frac{s+1}{s\left ( s+2 \right )}$The initial and final values, respectively, of the function are $0$ and $1$$1$ and $\frac{1}{2}$...

The Laplace transform of $e^{at}\sin\left ( bt \right )$ is$\frac{b}{\left ( s-a \right )^{2}+b^{2}}$$\frac{s-a}{\left ( s-a \right )^{2}+b^{2}}$$\frac{s-a}{\left ( s-a \...

What is the solution for the second order differential equation $\frac{\mathrm{d} ^{2}y}{\mathrm{d} x}^{2}+y=0$, with the initial conditions $y\left | _{x-0}=5\:and\:\fra...

Consider a linear ordinary differential equation: $\frac{dy}{dx}+p\left ( x \right )y=r\left ( x \right )$. Functions $p\left ( x \right )$ and $r\left ( x \right )$ are...

The differential equation $\frac{d^{2}y}{dx^{2}}+x^{2}\frac{dy}{dx}+x^{3}y=e^{x}$ is a non-linear differential equation of first degreelinear differential equation of fir...

The integrating factor for the differential equation$\frac{dy}{dx}-\frac{y}{1+x}=\left ( 1+x \right )$ is$\frac{1}{1+x}$$(1+x)$$x(1+x)$$\frac{x}{1+x}$

Consider the following differential equation$\frac{dy}{dx}=x+In\:\left ( y \right ); y=2 \: at \: x=0$The solution of this equation at $x=0.4$ using Euler method with a s...

For the time domain function $f(t)=t^{2}$, which $ONE$ of the following is the Laplace transform of $\int _{0}^{t}f\left ( t \right )dt$?$\frac{3}{s^{4}}$$\frac{1}{4s^{2}...

The solution of the differential equation$\frac{d^2y}{dx^2}$ – $\frac{dy}{dx}$ + 0.25y = 0, given y = 0 at x = 0 and $\frac{dy}{dx}$ = 1 at x = 0 isxe$^{0.5x}$ – xe$^{-0...

The solution of the differential equation$\frac{dy}{dx}$ – y$^{2}$ = 0, given y=1 at x=0 is$\frac{1}{1+x}$$\frac{1}{1-x}$$\frac{1}{(1-x)^2}$$\frac{x^3}{3}$+1

If $a$ and $b$ are arbitrary constants, then the solutions to the ordinary differential equation $\dfrac{d^...

Consider the following two equation:$\frac{dx}{dt}+x+y=0$$\frac{dy}{dt}-x=0$The above set of equations is represented by$\frac{d^{2}y}{dt^{2}}-\frac{dy}{dt}-y=0$$\frac{d^...