1
AIEEE 2004
+4
-1
The differential equation for the family of circle $${x^2} + {y^2} - 2ay = 0,$$ where a is an arbitrary constant is
A
$$\left( {{x^2} + {y^2}} \right)y' = 2xy$$
B
$$2\left( {{x^2} + {y^2}} \right)y' = xy$$
C
$$\left( {{x^2} - {y^2}} \right)y' =2 xy$$
D
$$2\left( {{x^2} - {y^2}} \right)y' = xy$$
2
AIEEE 2004
+4
-1
Solution of the differential equation $$ydx + \left( {x + {x^2}y} \right)dy = 0$$ is
A
$$log$$ $$y=Cx$$
B
$$- {1 \over {xy}} + \log y = C$$
C
$${1 \over {xy}} + \log y = C$$
D
$$- {1 \over {xy}} = C$$
3
AIEEE 2003
+4
-1
The solution of the differential equation

$$\left( {1 + {y^2}} \right) + \left( {x - {e^{{{\tan }^{ - 1}}y}}} \right){{dy} \over {dx}} = 0,$$ is
A
$$x{e^{2{{\tan }^{ - 1}}y}} = {e^{{{\tan }^{ - 1}}y}} + k$$
B
$$\left( {x - 2} \right) = k{e^{2{{\tan }^{ - 1}}y}}$$
C
$$2x{e^{{{\tan }^{ - 1}}y}} = {e^{2{{\tan }^{ - 1}}y}} + k$$
D
$$x{e^{{{\tan }^{ - 1}}y}} = {\tan ^{ - 1}}y + k$$
4
AIEEE 2003
+4
-1
The degree and order of the differential equation of the family of all parabolas whose axis is $$x$$-axis, are respectively.
A
$$2, 3$$
B
$$2,1$$
C
$$1,2$$
D
$$3,2.$$
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