1
GATE PI 2009
+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
+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
+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
+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
$$\,\left( {1 - t} \right){e^{ t}}$$
GATE PI Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Heat Transfer
Thermodynamics
Casting
Joining of Materials
Metal Forming
Machine Tools and Machining
Metrology
Industrial Engineering
EXAM MAP
Joint Entrance Examination