1
GATE ME 2005
+2
-0.6
The complete solution of the ordinary differential equation $${{{d^2}y} \over {d\,{x^2}}} + p{{dy} \over {dx}} + qy = 0$$ is $$\,y = {c_1}\,{e^{ - x}} + {C_2}\,{e^{ - 3x}}\,\,$$ then $$p$$ and $$q$$ are
A
$$p=3, q=3$$
B
$$p=3, q=4$$
C
$$p=4, q=3$$
D
$$p=4, q=4$$
2
GATE ME 2005
+2
-0.6
Which of the following is a solution of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + \left( {q + 1} \right)y = 0?$$ Where $$p=4, q=3$$
A
$${e^{ - 3x}}$$
B
$$x{e^{ - x}}$$
C
$$x$$ $${e^{ - 2x}}$$
D
$${x^2}\,{e^{ - 2x}}$$
3
GATE ME 2000
Subjective
+2
-0
Find the solution of the differential equation $$\,{{{d^2}u} \over {d{t^2}}} + {\lambda ^2}y = \cos \left( {wt + k} \right)$$ with initial conditions $$\,y\left( 0 \right) = 0,\,\,{{dy\left( 0 \right)} \over {dt}} = 0.$$ Here $$\lambda ,$$ $$w$$ and $$k$$ are constants. Use either the method of undetermined coefficients (or) the operator $$\left( {D = {\raise0.5ex\hbox{d} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{{dt}}}} \right)$$
4
GATE ME 1998
Subjective
+2
-0
The radial displacement in a rotating disc is governed by the differential equation $$\,\,{{{d^2}u} \over {d{x^2}}} + {1 \over x}{{du} \over {dx}} - {u \over {{x^2}}} = 8x.\,\,\,$$ where $$u$$ is the displacement and $$x$$ is the radius. If $$u=0$$ at $$x=0$$ and $$u=2$$ at $$x=1,$$ calculate the displacement at $$\,x = {1 \over {2.}}$$
GATE ME Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
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