1
GATE PI 2012
MCQ (Single Correct Answer)
+2
-0.6
Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ and $$\,\,y\left( 1 \right) = 1.\,\,\,$$ The complete solution of the differential equation is
A
$${x^2}$$
B
$$\sin \left( {{{\pi x} \over 2}} \right)$$
C
$${e^x}\sin \left( {{{\pi x} \over 2}} \right)$$
D
$${e^{ - x}}\sin \left( {{{\pi x} \over 2}} \right)$$
2
GATE PI 2011
MCQ (Single Correct Answer)
+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
$$y = \left( {{C_1}x + {C_2}} \right){e^{3x}} + x$$
3
GATE PI 2010
MCQ (Single Correct Answer)
+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 2010
MCQ (Single Correct Answer)
+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
$${{{d^2}y} \over {d{x^2}}} - 9y = 0$$
GATE PI Subjects
Engineering Mechanics
Theory of Machines
Machine Design
Fluid Mechanics
Thermodynamics
Casting
Joining of Materials
Metal Forming
Machine Tools and Machining
Metrology
Industrial Engineering
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
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Civil Services
UPSC Civil Service
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NDA
CBSE
Class 12
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