1
GATE PI 2009
MCQ (Single Correct Answer)
+1
-0.3
The homogeneous part of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + qy = r\,\,$$ ( $$p, q, r$$ are constants) has real distinct roots if
A
$${p^2} - 4q > 0$$
B
$${p^2} - 4q < 0$$
C
$${p^2} - 4q = 0$$
D
$${p^2} - 4q = r$$
2
GATE PI 2008
MCQ (Single Correct Answer)
+1
-0.3
The solutions of the differential equation $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$ are
A
$${e^{ - \left( {1 + i} \right)x}},{e^{ - \left( {1 - i} \right)x}}$$
B
$${e^{\left( {1 + i} \right)x}},\,\,{e^{\left( {1 - i} \right)x}}$$
C
$${e^{ - \left( {1 + i} \right)x}},\,\,{e^{\left( {1 + i} \right)x}}$$
D
$${e^{\left( {1 + i} \right)x}},\,\,{e^{ - \left( {1 + i} \right)x}}$$
3
GATE PI 2005
MCQ (Single Correct Answer)
+1
-0.3
The differential equation $${\left[ {1 + {{\left( {{{d\,y} \over {d\,x}}} \right)}^2}} \right]^3} = {C^2}{\left[ {{{{d^2}\,y} \over {d\,{x^2}}}} \right]^2}$$ is of
A
$${2^{nd}}$$ order and $${3^{rd}}$$ degree
B
$${3^{rd}}$$ order and $${2^{nd}}$$ degree
C
$${2^{nd}}$$ order and $${2^{nd}}$$ degree
D
$${3^{rd}}$$ order and $${3^{rd}}$$ degree
4
GATE PI 1994
MCQ (Single Correct Answer)
+1
-0.3
Solve for $$y$$ if $${{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0$$ with $$y(0)=1$$ and $${y^1}\left( 0 \right) = - 2$$
A
$$\,\left( {1 - t} \right){e^{ - t}}$$
B
$$\,\left( {1 + t} \right){e^{ t}}$$
C
$$\,\left( {1 + t} \right){e^{ - t}}$$
D
$$\,\left( {1 - t} \right){e^{ t}}$$
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