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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
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