1
GATE ME 2006
+1
-0.3
For $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 4{{dy} \over {dx}} + 3y = 3{e^{2x}},\,\,$$ the particular integral is
A
$${1 \over {15}}{e^{2x}}$$
B
$${1 \over {5}}{e^{2x}}$$
C
$$3{e^{2x}}$$
D
$${c_1}{e^{ - x}} + {c_2}{e^{ - 3x}}$$
2
GATE ME 2006
+1
-0.3
The solution of the differential equation $${{dy} \over {dx}} + 2xy = {e^{ - {x^2}}}\,\,$$ with $$y(0)=1$$ is
A
$$\left( {1 + x} \right)\,\,{e^{{x^2}}}$$
B
$$\left( {1 + x} \right)\,\,{e^{ - {x^2}}}$$
C
$$\left( {1 - x} \right)\,\,{e^{{x^2}}}$$
D
$$\left( {1 - x} \right)\,\,{e^{ - {x^2}}}$$
3
GATE ME 2005
+1
-0.3
If $${x^2}\left( {{{d\,y} \over {d\,x}}} \right) + 2xy = {{2\ln x} \over x}$$ and $$y(1)=0$$ then what is $$y(e)$$?
A
$$e$$
B
$$1$$
C
$${{1 \over e}}$$
D
$${{1 \over {{e^2}}}}$$
4
GATE ME 2003
+1
-0.3
The solution of the differential equation $${{dy} \over {dx}} + {y^2} = 0$$ is
A
$$y = {1 \over {x + c}}$$
B
$$y = - {{{x^3}} \over 3} + c$$
C
$$c\,\,{e^x}$$
D
unsolvable as equation is non-linear
GATE ME Subjects
EXAM MAP
Medical
NEET