1
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

he general solution of the differential equation $${\log _e}\left( {{{dy} \over {dx}}} \right) = x + y$$ is

A
$${e^x} + {e^{ - y}} = C$$
B
$${e^x} + {e^y} = C$$
C
$${e^y} + {e^{ - x}} = C$$
D
$${e^{ - x}} + {e^{ - y}} = C$$
2
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

The solution of $${{dy} \over {dx}} = {y \over x} + \tan {y \over x}$$ is

A
$$x = c\sin (y/x)$$
B
$$x = c\sin (xy)$$
C
$$y = c\sin (y/x)$$
D
$$xy = c\sin (x/y)$$
3
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

Integrating factor (I.F.) of the differential equation $${{dy} \over {dx}} - {{3{x^2}} \over {1 + {x^3}}}y = {{{{\sin }^2}x} \over {1 + x}}$$ is

A
$${e^{1 + {x^3}}}$$
B
$$\log (1 + {x^3})$$
C
$$1 + {x^3}$$
D
$${1 \over {1 + {x^3}}}$$
4
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

The differential equation of y = aebx (a & b are parameters) is

A
$$y{y_1} = y_2^2$$
B
$$y{y_2} = y_1^2$$
C
$$yy_1^2 = {y_2}$$
D
$$yy_2^2 = {y_1}$$
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