1
AIEEE 2009
+4
-1
Out of Syllabus
The differential equation which represents the family of curves $$y = {c_1}{e^{{c_2}x}},$$ where $${c_1}$$ , and $${c_2}$$ are arbitrary constants, is
A
$$y'' = y'y$$
B
$$yy'' = y'$$
C
$$yy'' = {\left( {y'} \right)^2}$$
D
$$y' = {y^2}$$
2
AIEEE 2008
+4
-1
The solution of the differential equation

$${{dy} \over {dx}} = {{x + y} \over x}$$ satisfying the condition $$y(1)=1$$ is :
A
$$y = \ln x + x$$
B
$$y = x\ln x + {x^2}$$
C
$$y = x{e^{\left( {x - 1} \right)}}\,$$
D
$$y = x\,\ln x + x$$
3
AIEEE 2007
+4
-1
Out of Syllabus
The differential equation of all circles passing through the origin and having their centres on the $$x$$-axis is :
A
$${y^2} = {x^2} + 2xy{{dy} \over {dx}}$$
B
$${y^2} = {x^2} - 2xy{{dy} \over {dx}}$$
C
$${x^2} = {y^2} + xy{{dy} \over {dx}}$$
D
$${x^2} = {y^2} + 3xy{{dy} \over {dx}}$$
4
AIEEE 2006
+4
-1
The differential equation whose solution is $$A{x^2} + B{y^2} = 1$$
where $$A$$ and $$B$$ are arbitrary constants is of
A
second order and second degree
B
first order and second degree
C
first order and first degree
D
second order and first degree
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