1
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
$${x^2} = {y^2} + 3xy{{dy} \over {dx}}$$
2
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
3
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 $$2$$
4
AIEEE 2005
+4
-1
If $$x{{dy} \over {dx}} = y\left( {\log y - \log x + 1} \right),$$ then the solution of the equation is :
A
$$y\log \left( {{x \over y}} \right) = cx$$
B
$$x\log \left( {{y \over x}} \right) = cy$$
C
$$\log \left( {{y \over x}} \right) = cx$$
D
$$\log \left( {{x \over y}} \right) = cy$$
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