1
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
$$y = x\,\ln x + x$$
2
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
$${x^2} = {y^2} + 3xy{{dy} \over {dx}}$$
3
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
4
AIEEE 2005
+4
-1
The differential equation representing the family of curves $${y^2} = 2c\left( {x + \sqrt c } \right),$$ where $$c>0,$$ is a parameter, is of order and degree as follows:
A
order $$1,$$ degree $$2$$
B
order $$1,$$ degree $$1$$
C
order $$1,$$ degree $$3$$
D
order $$2,$$ degree $$2$$
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