1
GATE ECE 2018
+2
-0.67
A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation

$${{dy} \over {dx}} = {{{x^2} + {y^2}} \over {2y}} + {y \over x}$$. The equation that describes the curve is
A
$$\ln \left( {1 + {{{y^2}} \over {{x^2}}}} \right) = x - 1$$
B
$${1 \over 2}\ln \left( {1 + {{{y^2}} \over {{x^2}}}} \right) = x - 1$$
C
$${1 \over 2}\ln \left( {1 + {y \over x}} \right) = x - 1$$
D
$$\ln \left( {1 + {y \over x}} \right) = x - 1$$
2
GATE ECE 2017 Set 1
+2
-0.6
Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left( {x + y - 1} \right)^2}$$ , where $$x,$$ $$y$$ are real ?
A
$$y = 1 + x + {\tan ^{ - 1}}\left( {x + c} \right),$$ where $$c$$ is a constant
B
$$y = 1 + x + \tan \left( {x + c} \right),$$ where $$c$$ is a constant
C
$$y = 1 - x + {\tan ^{ - 1}}\left( {x + c} \right),$$ where $$c$$ is a constant
D
$$y = 1 - x + \tan \left( {x + c} \right),$$ where $$c$$ is a constant
3
GATE ECE 2016 Set 3
+2
-0.6
The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}} + 36y = 0\,\,$$ with $$\,y\left( 0 \right) = 3\,\,$$ and $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 0}} = - 36\,\,$$
A
$$\left( {3 - 18x} \right){e^{ - 6x}}$$
B
$$\left( {3 + 25x} \right){e^{ - 6x}}$$
C
$$\left( {3 + 20x} \right){e^{ - 6x}}$$
D
$$\left( {3 - 12x} \right){e^{ - 6x}}$$
4
GATE ECE 2015 Set 3
Numerical
+2
-0
Consider the differential equation $${{{d^2}x\left( t \right)} \over {d{t^2}}} + 3{{dx\left( t \right)} \over {dt}} + 2x\left( t \right) = 0$$
Given $$x(0) = 20$$ & $$\,x\left( 1 \right) = {{10} \over e},$$ where $$e=2.718,$$

The value of $$x(2)$$ is