1
AIEEE 2010
+4
-1
Solution of the differential equation

$$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x <{\pi \over 2}$$ is :
A
$$y\sec x = \tan x + c$$
B
$$y\tan x = \sec x + c$$
C
$$\tan x = \left( {\sec x + c} \right)y$$
D
$$\sec x = \left( {\tan x + c} \right)y$$
2
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
$$y' = {y^2}$$
3
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
$$y = x\,\ln x + x$$
4
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
$${x^2} = {y^2} + 3xy{{dy} \over {dx}}$$
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