1
GATE ME 2007
+1
-0.3
The partial differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} + {{\partial \phi } \over {\partial x}} + {{\partial \phi } \over {\partial y}} = 0\,\,\,\,$$ has
A
degree $$1$$ and order $$2$$
B
degree $$1$$ and order $$1$$
C
degree $$2$$ and order $$1$$
D
degree $$2$$ and order $$2$$
2
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
$${c_1}{e^{ - x}} + {c_2}{e^{ - 3x}}$$
3
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
$$\left( {1 - x} \right)\,\,{e^{ - {x^2}}}$$
4
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
$${{1 \over {{e^2}}}}$$
GATE ME Subjects
EXAM MAP
Medical
NEET