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NIELIT 2017 OCT Scientific Assistant A (IT) - Section D: 6
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$e^{-2t}u(t)$e^{2t}u(t)$e^{-t}u(t)$e^{t}u(t)$
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NIELIT 2017 OCT Scientific Assistant A (CS) - Section D: 6
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$e^{-2t}u(t)$e^{2t}u(t)$e^{-t}u(t)$e^{t}u(t)$
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NIELIT 2016 MAR Scientist B - Section B: 15
Differential equation, $\dfrac{d^2x}{dt^2}+10\dfrac{dx}{dt}+25x=0$ will have a solution of the form $(C_1+C_2t)e^{-5t}$C_1e^{-2t}$C_1e^{-5t}+C_2e^{5t}$C_1e^{-5t}+C_2e^{2t}$where $C_1$ and $C_2$ are constants.
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ISI2015-MMA-85
The differential equation of all the ellipses centred at the origin is$y^2+x(y’)^2-yy’=0$xyy’’ +x(y’)^2 -yy’=0$yy’’+x(y’)^2-xy’=0$none of these
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ISI2015-MMA-87
If $x(t)$ is a solution of $(1-t^2) dx -tx\: dt =dt$ and $x(0)=1$, then $x\big(\frac{1}{2}\big)$ is equal to$\frac{2}{\sqrt{3}} (\frac{\pi}{6}+1)$\frac{2}{\sqrt{3}} (\frac{\pi}{6}-1)$\frac{\pi}{3 \sqrt{3}}$\frac{\pi}{\sqrt{3}}$
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ISI2015-MMA-88
Let $f(x)$ be a given differentiable function. Consider the following differential equation in $y$ $f(x) \frac{dy}{dx} = yf'(x)-y^2.$ The general solution of this equation is given ... $y=\frac{\left[f(x)\right]^2}{x+c}$
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ISI2015-MMA-89
Let $y(x)$ be a non-trivial solution of the second order linear differential equation $\frac{d^2y}{dx^2}+2c\frac{dy}{dx}+ky=0,$ where $c<0$, $k>0$ ... exists and is finitenone of the above is true
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ISI2015-MMA-90
The differential equation of the system of circles touching the $y$-axis at the origin is$x^2+y^2-2xy \frac{dy}{dx}=0$x^2+y^2+2xy \frac{dy}{dx}=0$x^2-y^2-2xy \frac{dy}{dx}=0$x^2-y^2+2xy \frac{dy}{dx}=0$
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ISI2015-MMA-91
Suppose a solution of the differential equation $(xy^3+x^2y^7)\frac{\mathrm{d} y}{\mathrm{d} x}=1,$ satisfies the initial condition $y(1/4)=1$ ... $- \frac{4}{3}$\frac{16}{5}$- \frac{16}{5}$
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ISI2016-DCG-67
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration)$x^{2}-y^{2}=C$2x^{2}-y^{2}=C$2y^{2}-x^{2}=C$x^{2}+y^{2}=C$
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ISI2016-DCG-68
The general solution of the differential equation $x+y-x{y}'=0$ is (assuming $C$ as an arbitrary constant of integration)$y=x(\log x+C)$x=y(\log y+C)$y=x(\log y+C)$y=y(\log x+C)$
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ISI2016-DCG-69
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is$x^{2}+(y-5)^{2}=25$x^{2}+y^{2}=100$(x-5)^{2}+y^{2}=125$(x-5)^{2}+(y-5)^{2}=50$
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ISI2017-DCG-24
The differential equation $x \frac{dy}{dx} -y=x^3$ with $y(0)=2$ hasunique solutionno solutioninfinite number of solutionsnone of these
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ISI2018-MMA-25
The solution of the differential equation$(1 + x^2y^2)ydx + (x^2y^2 − 1)xdy = 0$ is$xy = \log\ x − \log\ y + C$xy = \log\ y − \log\ x + C$x^2y^2 = 2(\log\ x − \log\ y) + C$x^2y^2 = 2(\log\ y − \log\ x) + C$
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ISI2019-MMA-18
For the differential equation $\frac{dy}{dx} + xe^{-y}+2x=0$It is given that $y=0$ when $x=0$. When $x=1$, $\:y$ ... - \frac{1}{2} \bigg)$\text{ln} \bigg(\frac{3}{2e} - \frac{1}{4} \bigg)$
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ISI2019-MMA-6
The solution of the differential equation $\frac{dy}{dx} = \frac{2xy}{x^2-y^2}$is$x^2 + y^2 = cy$, where $c$ is a constant$x^2 + y^2 = cx$, where $c$ is a ... $c$ is a constant$x^2 - y^2 = cx$, where $c$ is a constant
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NIELIT 2018-18
If $y^a$ is an integrating factor of the differential equation $2xydx-(3x^2-y^2)dy=0$, then the value of $a$ is$-4$4$-1$1$
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NIELIT 2018-20
The general solution of the differential equation $\frac{dy}{dx} = (1+y^2)(e^{-x^2}-2x \tan^{-1} y)$ is:$e^{x^2} \tan^{-1} y = x+c$e^{-x^2} \tan^y = x+c$e^x \tan y = x^2+c$e^{-x} \tan^{-1} y = x^3+c$
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NIELIT 2018-22
While solving the differential equation $\frac{d^2 y}{dx^2} +4y = \tan 2x$ by the method of variation of parameters, then value of Wronskion (W) is:$1$2$3$4$
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NIELIT 2018-25
The general solution of the partial differential equation $(D^2-D'^2-2D+2D')Z=0$ where $D= \frac{\partial}{\partial x}$ and $D'=\frac{\partial}{\partial y}$:$f(y+x)+e^{2x}g(y-x)$e^{2x ... $f(y+x)+e^{-2x}g(y-x)$
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ISI2017-MMA-9
A function $y(x)$ that satisfies $\dfrac{dy}{dx}+4xy=x$ with the boundary condition $y(0)=0$ is$y(x)=(1-e^x)$y(x)=\frac{1}{4}(1-e^{-2x^2})$y(x)=\frac{1}{4}(1-e^{2x^2})$y(x)=\frac{1}{4}(1-\cos x)$
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ISI2016-MMA-7
The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$ is$\{1\}$\{1, -1\}$\{1, 2\}$\{-1, 2\}$
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virtual gate
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TIFR CSE 2012 | Part A | Question: 15
Consider the differential equation $dx/dt= \left(1 - x\right)\left(2 - x\right)\left(3 - x\right)$. Which of its equilibria is unstable?$x=0$x=1$x=2$x=3$None of the above
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GATE CSE 1993 | Question: 01.2
The differential equation $\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0$ is:linearnon- linear homogeneousof degree two
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