1
AIEEE 2003
MCQ (Single Correct Answer)
+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
$$x{e^{{{\tan }^{ - 1}}y}} = {\tan ^{ - 1}}y + k$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+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
$$3,2.$$
3
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
The order and degree of the differential equation
$$\,{\left( {1 + 3{{dy} \over {dx}}} \right)^{2/3}} = 4{{{d^3}y} \over {d{x^3}}}$$ are
A
$$\left( {1,{2 \over 3}} \right)$$
B
$$(3, 1)$$
C
$$(3,3)$$
D
$$(1,2)$$
4
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
The solution of the equation $$\,{{{d^2}y} \over {d{x^2}}} = {e^{ - 2x}}$$
A
$${{{e^{ - 2x}}} \over 4}$$
B
$${{{e^{ - 2x}}} \over 4} + cx + d$$
C
$${1 \over 4}{e^{ - 2x}} + c{x^2} + d$$
D
$$\,{1 \over 4}{e^{ - 4x}} + cx + d$$
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