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Recent questions tagged ordinary-differential-equation

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GATE Civil 2021 Set 2 | Question: 26
If $\text{k}$ is a constant, the general solution of $\dfrac{dy}{dx}-\dfrac{y}{x}=1$ will be in the form of $y=x\text{ ln}(kx)$ $y=k\text{ ln}(kx)$ $y=x\text{ ln}(x)$ $y=xk\text{ ln}(k)$

go_editor asked in Ordinary Differential Equation (ODE) Mar 1, 2021

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GATE Civil 2021 Set 1 | Question: 26
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 $e^{-x}+\left ( 3e-1 \right )xe^{-x}$ ... $e^{-x}-\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) -1\right ]xe^{-x}$

Arjun asked in Ordinary Differential Equation (ODE) Feb 20, 2021

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GATE2020-CE-1-26
For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}-5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the solution is $-5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $-10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$

go_editor asked in Ordinary Differential Equation (ODE) Feb 28, 2020

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GATE2020 CE-2-1
The ordinary differential equation $\dfrac{d^2u}{dx^2}$- 2x^2u +\sin x = 0$ is linear and homogeneous linear and nonhomogeneous nonlinear and homogeneous nonlinear and nonhomogeneous

go_editor asked in Ordinary Differential Equation (ODE) Feb 13, 2020

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GATE2020 CE-2-26
An ordinary differential equation is given below $6\dfrac{d^2y}{dx^2}+\frac{dy}{dx}-y=0$ The general solution of the above equation (with constants $C_1$ and $C_2$), is $y(x) = C_1e^\frac{-x}{3} + C_2e^\frac{x}{2}$ $y(x) = C_1e^\frac{x}{3} + C_2e^\frac{-x}{2}$ $ y(x) = C_1xe^\frac{-x}{3} + C_2e^\frac{x}{2}$ $ y(x) = C_1e^\frac{-x}{3} + C_2xe^\frac{x}{2}$

go_editor asked in Ordinary Differential Equation (ODE) Feb 13, 2020

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GATE2017 CE-2-29
Consider the following second-order differential equation: $y’’ – 4y’+3y =2t -3t^2$. The particular solution of the differential solution equation is $ – 2 -2t-t^2$ $ – 2t-t^2$ $2t-3t^2$ $ – 2 -2t-3 t^2$

gatecse asked in Partial Differential Equation (PDE) Aug 7, 2019

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GATE2019 CE-1: 44
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 off to $1$ decimal place), is _________

Arjun asked in Ordinary Differential Equation (ODE) Feb 14, 2019

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8

GATE2019 CE-2: 2
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2-a^2} \\$ $\dfrac{a}{s^2 + a^2} \\$ $\dfrac{s}{s^2-a^2} \\$ $\dfrac{s}{s^2+a^2}$

Arjun asked in Ordinary Differential Equation (ODE) Feb 12, 2019

by Arjun

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GATE2019 CE-2: 28
An ordinary differential equation is given below; $\left ( \dfrac{dy}{dx} \right ) (x \text{ ln } x)=y$ The solution for the above equation is (Note: $K$ denotes a constant in the options) $y=K x \text{ ln } x$ $y=K x e^x$ $y=K x e^{-x}$ $y=K \text{ ln } x$

Arjun asked in Ordinary Differential Equation (ODE) Feb 12, 2019

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10

GATE2016-1-30
The respective expressions for complementary function and particular integral part of the solution of the differential equation $\dfrac{d^4y}{dx^4}+3 \dfrac{d^2y}{dx^2} = 108x^2$ are $\lfloor c_1+c_2x+c_3 \sin \sqrt{3}x+c_4 \cos \sqrt{3} x \rfloor$ ... $\lfloor c_1+c_2x+c_3 \sin \sqrt{3}x+c_4 \cos \sqrt{3} x \rfloor$ and $\lfloor 5x^4 - 12x^2 +c \rfloor$

Milicevic3306 asked in Ordinary Differential Equation (ODE) Mar 28, 2018

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11

GATE2017 CE-1: 27
The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is $Q(t)=e^{-t}-1$ $Q(t)=1+ e^{-t}$ $Q(t)=1 -e^t$ $Q(t)=1- e^{-t}$

Milicevic3306 asked in Ordinary Differential Equation (ODE) Mar 26, 2018

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12

GATE2017 CE-1: 37
Consider the equation $\dfrac{du}{dt}=3t^2+1$ with $u=0$ at $t=0$. This is numerically solved by using the forward Euler method with a step size, $\Delta t=2$. The absolute error in the solution at the end of the first time step is _______.

Milicevic3306 asked in Ordinary Differential Equation (ODE) Mar 26, 2018

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13

GATE2015-2-27
Consider the following second order linear differential equation $\dfrac{d^2y}{dx^2} = -12x^2 +24 x – 20$ The boundary conditions are: at $x=0, \: y=5$ and at $x=2, \: y=21$. The value of $y$ at $x=1$ is _________.

Milicevic3306 asked in Ordinary Differential Equation (ODE) Mar 26, 2018

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14

GATE2015-1-28
Consider the following differential equation: $x(y\:dx +x\:dy) \cos \dfrac{y}{x}=y(x\:dy-y\:dx) \sin \dfrac{y}{x}$ Which of the following is the solution of the above equation ($c$ is an arbitrary constant)? $\dfrac{x}{y} \cos \dfrac{y}{x} = c \\$ $\dfrac{x}{y} \sin \dfrac{y}{x} = c \\$ $xy \cos \dfrac{y}{x} = c \\$ $xy \sin \dfrac{y}{x} = c$

Milicevic3306 asked in Ordinary Differential Equation (ODE) Mar 26, 2018

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15

GATE2014-2-4
The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is $e^{-k_1t} \\$ $e^{-k_2t} \\$ $e^{k_1t} \\$ $e^{k_2t}$

Milicevic3306 asked in Ordinary Differential Equation (ODE) Mar 26, 2018

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16

GATE Civil 2012 | Question: 30
The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is $y=e^{-2x}$ $y=2e^{-2x}$ $y=10.95 e^{-2x}$ $y=36.95 e^{-2x}$

Milicevic3306 asked in Ordinary Differential Equation (ODE) Mar 25, 2018

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17

GATE2018 CE-2: 27
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(s-a) >0$, is $\dfrac{1}{s+a} \\$ $\dfrac{1}{s-a} \\$ $\dfrac{1}{a-s} \\$ $\infty$

gatecse asked in Ordinary Differential Equation (ODE) Feb 17, 2018

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18

GATE2018 CE-2: 1
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is $x$ $x^2$ $x^{-1}$ $x^{-2}$

gatecse asked in Ordinary Differential Equation (ODE) Feb 17, 2018

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19

GATE2018 CE-1: 38
The solution (up to three decimal places) at $x=1$ of the differential equation $\dfrac{d^2y}{dx^2} + 2 \dfrac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ and $\dfrac{dy}{dx}(0) = -1$ is _____

gatecse asked in Ordinary Differential Equation (ODE) Feb 17, 2018

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