1
GATE IN 2014
MCQ (Single Correct Answer)
+1
-0.3
The figure shows the plot of $$y$$ as a function of $$x$$ GATE IN 2014 Engineering Mathematics - Differential Equations Question 2 English

The function shown in the solution of the differential equation (assuming all initial conditions to be zero) is

A
$${{{d^2}y} \over {d{x^2}}} = 1$$
B
$${{dy} \over {dx}} = + x$$
C
$${{dy} \over {dx}} = - x$$
D
$${{dy} \over {dx}} = \left| x \right|$$
2
GATE IN 2013
MCQ (Single Correct Answer)
+1
-0.3
The type of the partial differential equation $${{\partial f} \over {\partial t}} = {{{\partial ^2}f} \over {\partial {x^2}}}\,\,is$$
A
Parabolic
B
Elliptic
C
Hyperbolic
D
Nonlinear
3
GATE IN 2012
MCQ (Single Correct Answer)
+1
-0.3
With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is
A
$$x = t - {1 \over 2}$$
B
$$x = {t^2} - {1 \over 2}$$
C
$$xt = {{{t^2}} \over 2}$$
D
$$x = {t \over 2}$$
4
GATE IN 2010
MCQ (Single Correct Answer)
+1
-0.3
Consider the differential equation $${{dy} \over {dx}} + y = {e^x}$$ with $$y(0)=1.$$ Then the value of $$y(1)$$ is
A
$$e + {e^{ - 1}}$$
B
$${1 \over 2}\left[ {e - {e^{ - 1}}} \right]$$
C
$${1 \over 2}\left[ {e + {e^{ - 1}}} \right]$$
D
$$2\left[ {e - {e^{ - 1}}} \right]$$
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