1
GATE ME 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Find the solution of $${{{d^2}y} \over {d{x^2}}} = y$$ which passes through origin and the point $$\left( {ln2,{3 \over 4}} \right)$$
A
$$y = {1 \over 2}{e^x} - {e^{ - x}}$$
B
$${1 \over 2}\left( {{e^x} + {e^{ - x}}} \right)$$
C
$$y = {1 \over 2}\left( {{e^x} - {e^{ - x}}} \right)$$
D
$${1 \over 2}{e^x} + {e^{ - x}}$$
2
GATE ME 2014 Set 4
MCQ (Single Correct Answer)
+1
-0.3
The solution of the initial value problem $$\,\,{{dy} \over {dx}} = - 2xy;y\left( 0 \right) = 2\,\,\,$$ is
A
$$1 + {e^{ - {x^2}}}$$
B
$$2{e^{ - {x^2}}}$$
C
$$1 + {e^{ {x^2}}}$$
D
$$2{e^{ {x^2}}}$$
3
GATE ME 2013
MCQ (Single Correct Answer)
+1
-0.3
The partial differential equation $$\,\,{{\partial u} \over {\partial t}} + u{{\partial u} \over {\partial x}} = {{{\partial ^2}u} \over {\partial {x^2}}}\,\,\,$$ is a
A
Linear equation of order $$2$$
B
Non-linear equation of order $$1$$
C
Linear equation of order $$1$$
D
non-linear equation of order $$2$$
4
GATE ME 2011
MCQ (Single Correct Answer)
+1
-0.3
Consider the differential equation $${{dy} \over {dx}} = \left( {1 + {y^2}} \right)x\,\,.$$ The general solution with constant $$'C'$$ is
A
$$y = \tan \left( {{{{x^2}} \over 2}} \right) + C$$
B
$$y = {\tan ^2}\left( {{x \over 2} + C} \right)$$
C
$$y = {\tan ^2}\left( {{x \over 2}} \right) + C$$
D
$$y = \tan \left( {{{{x^2}} \over 2} + C} \right)$$
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