1
GATE ME 2007
MCQ (Single Correct Answer)
+1
-0.3
The solution of $${{d\,y} \over {d\,x}} = {y^2}$$ with initial value $$y(0)=1$$ is bounded in the interval is
A
$$ - \infty \le x \le \propto $$
B
$$ - \infty \le x \le 1$$
C
$$x < 1,x > 1$$
D
$$ - 2 \le x \le 2$$
2
GATE ME 2007
MCQ (Single Correct Answer)
+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 $$2$$
3
GATE ME 2006
MCQ (Single Correct Answer)
+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
$${c_1}{e^{ - x}} + {c_2}{e^{ - 3x}}$$
4
GATE ME 2006
MCQ (Single Correct Answer)
+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
$$\left( {1 - x} \right)\,\,{e^{ - {x^2}}}$$
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