1
GATE CE 2017 Set 1
Numerical
+1
-0
Consider the following partial differential equation: $$\,\,3{{{\partial ^2}\phi } \over {\partial {x^2}}} + B{{{\partial ^2}\phi } \over {\partial x\partial y}} + 3{{{\partial ^2}\phi } \over {\partial {y^2}}} + 4\phi = 0\,\,$$ For this equation to be classified as parabolic, the value of $${B^2}$$ must be ____________.
Your input ____
2
GATE CE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The type of partial differential equation $${{{\partial ^2}p} \over {\partial {x^2}}} + {{{\partial ^2}p} \over {\partial {y^2}}} + 3{{{\partial ^2}p} \over {\partial x\partial y}} + 2{{\partial p} \over {\partial x}} - {{\partial p} \over {\partial y}} = 0$$ is
A
elliptic
B
parabolic
C
hyperbolic
D
none of these
3
GATE CE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The integrating factor for the differential equation $${{dP} \over {dt}} + {k_2}\,P = {k_1}{L_0}{e^{ - {k_1}t}}\,\,$$ is
A
$${e^{ - {k_1}t}}\,$$
B
$${e^{ - {k_2}t}}\,$$
C
$${e^{ {k_1}t}}\,$$
D
$${e^{ {k_2}t}}\,$$
4
GATE CE 2011
MCQ (Single Correct Answer)
+1
-0.3
The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$x=1$$ is
A
$$y = {2 \over {3{x^2}}} + {x \over 3}$$
B
$$y = {x \over 2} + {1 \over {2x}}$$
C
$$y = {2 \over 3} + {x \over 3}$$
D
$$y = {2 \over {3x}} + {{{x^2}} \over 3}$$
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