1
GATE IN 2012
+1
-0.3
With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is
A
$$x = t - {1 \over 2}$$
B
$$x = {t^2} - {1 \over 2}$$
C
$$xt = {{{t^2}} \over 2}$$
D
$$x = {t \over 2}$$
2
GATE IN 2010
+1
-0.3
Consider the differential equation $${{dy} \over {dx}} + y = {e^x}$$ with $$y(0)=1.$$ Then the value of $$y(1)$$ is
A
$$e + {e^{ - 1}}$$
B
$${1 \over 2}\left[ {e - {e^{ - 1}}} \right]$$
C
$${1 \over 2}\left[ {e + {e^{ - 1}}} \right]$$
D
$$2\left[ {e - {e^{ - 1}}} \right]$$
3
GATE IN 2008
+1
-0.3
Consider the differential equation $${{dy} \over {dx}} = 1 + {y^2}.$$ Which one of the following can be particular solution of this differential equation ?
A
$$y = tan(x+3)$$
B
$$y=(tanx)+3$$
C
$$x=tan(y+3)$$
D
$$x=(tany)+3$$
4
GATE IN 2005
+1
-0.3
The general solution of the differential equation $$\left( {{D^2} - 4D + 4} \right)y = 0$$ is of the form (given $$D = {d \over {dx}}$$ and $${C_1},{C_2}$$ are constants)
A
$${C_1}\,{e^{2x}}$$
B
$${C_1}\,{e^{2x}} + {C_2}\,{e^{ - 2x}}$$
C
$${C_1}\,{e^{2x}} + {C_2}\,{e^{2x}}$$
D
$${C_1}\,{e^{2x}} + {C_2}\,x\,{e^{2x}}$$
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