1
GATE PI 2011
+2
-0.6
The solution of the differential equation $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 6{{dy} \over {dx}} + 9y = 9x + 6\,\,\,\,$$ with $${C_1}$$ and $${C_2}$$ as constants is
A
$$y = \left( {{C_1}x + {C_2}} \right){e^{ - 3x}}$$
B
$$y = {C_1}\,{e^{3x}} + {C_2}\,{e^{ - 3x}}$$
C
$$y = \left( {{C_1}x + {C_2}} \right){e^{ - 3x}} + x$$
D
$$y = \left( {{C_1}x + {C_2}} \right){e^{3x}} + x$$
2
GATE PI 2010
+2
-0.6
Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$
A
$${{dy} \over {dx}} - {5 \over 3}\cos \left( {3x} \right) = 0$$
B
$${{dy} \over {dx}} + {5 \over 3}\left( {\cos 3x} \right) = 0$$
C
$${{{d^2}y} \over {{d^2}\,x}} + 9y = 0$$
D
$${{{d^2}y} \over {d{x^2}}} - 9y = 0$$
3
GATE PI 2010
+2
-0.6
The solution of the differential equation $${{dy} \over {dx}} - {y^2} = 1$$ satisfying the condition $$y(0)=1$$ is
A
$$y = {e^{{x^2}}}$$
B
$$y = \sqrt x$$
C
$$\,y = \cot \left( {x + {\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}} \right)$$
D
$$y = tan\left( {x + {\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}} \right)$$
4
GATE PI 2009
+2
-0.6
The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ with boundary conditions
(i) $${{dy} \over {dx}} = 1$$ at $$x=0$$
(ii) $${{dy} \over {dx}} = 1$$ at $$x=1$$
A
$$y=1$$
B
$$y=x$$
C
$$y=x+c$$ where $$c$$ is an arbitrary constant.
D
$$\,y = {C_1}x + {C_2}$$ where $${C_1},\,{C_2}$$ are arbitrary constants
GATE PI Subjects
Fluid Mechanics
Metrology
Theory of Machines
Machine Tools and Machining
Industrial Engineering
Engineering Mechanics
Thermodynamics
Machine Design
Casting
Joining of Materials
Metal Forming
EXAM MAP
Medical
NEET