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Recent questions and answers in Differential Equations
0
votes
0
answers
1
GATE2013-36
$\displaystyle{}\oint \frac{z^2-4}{z^2+4}\: dz$ evaluated anticlockwise around the circle $\mid z-i \mid=2$ , where $i=\sqrt{-1}$, is $-4\pi$ $0$ $2+\pi$ $2+2i$
asked
Feb 12, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2013-ee
integral
equations
0
votes
0
answers
2
GATE2014-2-26
To evaluate the double integral $\int_{0}^{8}(\int_{(y/2)}^{y/2+1}(\frac{2x-y}{2})dx)dy$ , we make the substitution $u=(\frac{2x-y}{2})$ and $v=\frac{y}{2}$ The integral will reduce $\int_{0}^{4}(\int_{0}^{2}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}udu) dv$ $\int_{0}^{4}(\int_{0}^{2}udu) dv$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
integral
upper-limit
lower-limit
0
votes
0
answers
3
GATE2014-2-5
Consider the differential equation $x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0$ . Which of the following is a solution to this differential equation for$x>0$? $e^x$ $x^2$ $1/x$ $lnx$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
derivatives
equations
0
votes
0
answers
4
GATE2014-1-17
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of only one root at the origin Imaginary roots only positive real roots only negative real roots
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
routh-hurwitz
array
polynomial
0
votes
0
answers
5
GATE2014-1-3
The solution for the differential equation $\dfrac{d^2x}{dt^2}=-9x,$ with initial conditions $x(0)=1$ and $\dfrac{dx}{dt}\mid_{t=0}=1$ , is $t^2+t+1$ $\sin3t+\frac{1}{3}\cos3t+\frac{2}{3}$ $\frac{1}{3}\sin3t+\cos3t$ $\cos3t+t$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
boundary-limits
differential
equation
0
votes
0
answers
6
GATE2014-1-2
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is $e^{-1}$ $e$ $1-e^{-1}$ $1+e^{-1}$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
interval
functions
0
votes
0
answers
7
GATE2015-2-28
A differential equation $\frac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2015-ee-2
non-linear-equation
eulers-equation
numerical-answers
0
votes
0
answers
8
GATE2015-1-27
A solution of the ordinary differential equation $\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\frac{1-3e}{e^{3}}$. The value of $\frac{dy}{dt}(0)$ is _______.
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2015-ee-1
ordinary-differential-equation
numerical-answers
0
votes
0
answers
9
GATE2016-2-30
Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then the value of $y(1)$ is _________.
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2016-ee-2
quadratic-equation
boundary-limits
numerical-answers
0
votes
0
answers
10
GATE2016-2-8
The solution of the differential equation, for $t > 0, y"(t)+2y'(t)+y(t)=0$ with initial conditions $y(0)=0$ and $y'(0)=1$, is ($u(t)$ denotes the unit step function), $te^{-t}u(t)$ $(e^{-t}-te^{-t})u(t)$ $(-e^{-t}+te^{-t})u(t)$ $e^{-t}u(t)$
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2016-ee-2
higher-order-differential-equations
euler's-equation
initial-boundary-conditions
0
votes
0
answers
11
GATE2016-2-4
Consider a causal $LTI$ system characterized by differential equation $\frac{dy(t)}{dt}+\frac{1}{6}y(t)=3x(t)$ The response of the system to the input $x(t)=3e^{-\frac{t}{3}}u(t)$, where $u(t)$ denotes the unit step function, is $9e^{-\frac{t}{3}}u(t)$ $9e^{-\frac{t}{6}}u(t)$ $9e^{-\frac{t}{3}}u(t)-6e^{-\frac{t}{6}}u(t)$ $54e^{-\frac{t}{6}}u(t)-54e^{-\frac{t}{3}}u(t)$
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2016-ee-2
function
derivative
numerical methods
0
votes
0
answers
12
GATE2016-1-4
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation $\frac{d^{2}y}{dt^{2}}+2\frac{dy}{dt}+y=0$. Then $y(2)$ is $5e^{-1}$ $5e^{-2}$ $7e^{-1}$ $7e^{-2}$
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2016-ee-1
quadratic-equation
repeated-roots
linear-ordinary-differential-equation
0
votes
0
answers
13
GATE2016-1-1
The maximum value attained by the function. $f(x) = x(x-1) (x-2)$ in the interval $[1, 2]$ is ___________.
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2016-ee-1
maxima
minima
critical-point
closed-interval
numerical-answers
0
votes
0
answers
14
GATE2016-1-5
The value of the integral $\oint _{c}\frac{2z+5}{\left ( z-\frac{1}{2} \right ) \left (z^{2} -4z+5 \right )}dz$ over the contour $|z|=1$, taken in the anti-clockwise direction, would be $\frac{24 \pi i}{13}$ $\frac{48 \pi i}{13}$ $\frac{24}{13}$ $\frac{12}{13}$
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2016-ee-1
partial-derivative
upper-limit
lower-limit
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