1
GATE ME 1995
True or False
+1
-0
A differential equation of the form $${{dy} \over {dx}} = f\left( {x,y} \right)\,\,$$ is homogeneous if the function $$f(x,y)$$ depends only on the ratio $${y \over x}$$ (or) $${x \over y}$$
A
TRUE
B
FALSE
2
GATE ME 1994
+1
-0.3
For the differential equation $$\,\,{{dy} \over {dt}} + 5y = 0\,\,$$ with $$y(0)=1,$$ the general solution is
A
$${e^{5t}}$$
B
$${e^{ - 5t}}$$
C
$$5$$ $${e^{ - 5t}}$$
D
$${e^{\sqrt { - 5t} }}$$
3
GATE ME 1993
Fill in the Blanks
+1
-0
The differential equation $${y^{11}} + y = 0\,$$ is subjected to the conditions $$y(0) = 0,$$ $$\,\,\,y\left( \lambda \right) = 0.\,\,$$ In order that the equation has non-trivial solutions, the general value of $$\lambda$$ is.
4
GATE ME 1993
+1
-0.3
The differential $$\,\,\,{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} + \sin y = 0\,\,$$ is
A
linear
B
non-linear
C
homogeneous
D
of degree two
GATE ME Subjects
Engineering Mechanics
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude
EXAM MAP
Joint Entrance Examination