1
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The general solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} - 5y = 0\,\,\,$$ in terms of arbitrary constants $${K_1}$$ and $${K_2}$$ is
A
$${K_1}{e^{\left( { - 1 + \sqrt 6 } \right)x}} + {K_2}{e^{\left( { - 1 - \sqrt 6 } \right)x}}$$
B
$${K_1}{e^{\left( { - 1 + \sqrt 8 } \right)x}} + {K_2}{e^{\left( { - 1 - \sqrt 8 } \right)x}}$$
C
$${K_1}{e^{\left( { - 2 + \sqrt 6 } \right)x}} + {K_2}{e^{\left( { - 2 - \sqrt 6 } \right)x}}$$
D
$${K_1}{e^{\left( { - 2 + \sqrt 8 } \right)x}} + {K_2}{e^{\left( { - 2 - \sqrt 8 } \right)x}}$$
2
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The general solution of the differential equation $$\,\,{{dy} \over {dx}} = {{1 + \cos 2y} \over {1 - \cos 2x}}\,\,$$ is
A
$$\,\,\tan \,y - \cot \,x = C\,\,$$
B
$$\tan \,x - \cot \,y = C\,$$
C
$$\,\,\tan \,y + \cot \,x = C\,\,$$
D
$$\tan \,x + \cot \,y = C\,$$
3
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the differential equation $$\,\,{{dx} \over {dt}} = 10 - 0.2\,x$$ with initial condition $$x(0)=1.$$ The response $$x(t)$$ for $$t > 0$$ is
A
$$2 - {e^{ - 0.2t}}$$
B
$$2 - {e^{ 0.2t}}$$
C
$$50 - 49\,{e^{ - 0.2t}}$$
D
$$50 - 49\,{e^{ 0.2t}}$$
4
GATE ECE 2014 Set 4
MCQ (Single Correct Answer)
+1
-0.3
If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{{dx} \over {dt}} + x = 0$$ is
A
$$a{e^{ - t}}$$
B
$$a{e^{ - t}} + bt{e^{ - t}}$$
C
$$a{e^t} + bt{e^{ - t}}$$
D
$$a{e^{ - 2t}}$$
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