1
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the following second $$-$$order differential equation : $$\,y''\,\, - 4y' + 3y = 2t - 3{t^2}\,\,\,$$
The particular solution of the differential equation is
A
$$ - 2 - 2t - {t^2}$$
B
$$ - 2t - {t^2}$$
C
$$2t - 3{t^2}$$
D
$$ - 2 - 2t - 3{t^2}$$
2
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 ____
3
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
4
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
$${e^{ {k_2}t}}\,$$
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