1
GATE CE 2016 Set 1
+2
-0.6
The solution of the partial differential equation $${{\partial u} \over {\partial t}} = \alpha {{{\partial ^2}u} \over {\partial {x^2}}}$$ is of the form
A
$$C\cos \left( {kt} \right)\left[ {{C_1}{e^{\left( {\sqrt {k/\alpha } } \right)x}} + {C_2}{e^{ - \left( {\sqrt {k/\alpha } } \right)x}}} \right]$$
B
$$C\,{e^{kt}}\left[ {{C_1}{e^{\left( {\sqrt {k/\alpha } } \right)x}} + {C_2}{e^{ - \left( {\sqrt {k/\alpha } } \right)x}}} \right]$$
C
$$C{e^{kt}}\left[ {{C_1}\,\cos \left( {\sqrt {k/\alpha } } \right)x + {C_2}\,\sin \left( { - \sqrt {k/\alpha } } \right)x} \right]$$
D
$$C\sin \left( {kt} \right)\left[ {{C_1}\,\cos \left( {\sqrt {k/\alpha } } \right)x + {C_2}\,\sin \left( { - \sqrt {k/\alpha } } \right)x} \right]$$
2
GATE CE 2015 Set 2
Numerical
+2
-0
Consider the following second order linear differential equation $${{{d^2}y} \over {d{x^2}}} = - 12{x^2} + 24x - 20$$
The boundary conditions are: at $$x=0, y=5$$ and at $$x=2, y=21$$
The value of $$y$$ at $$x=1$$ is
3
GATE CE 2015 Set 1
+2
-0.6
Consider the following differential equation
$$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$
$$\,\,\,\,\,\,\,\,\,\, = y\left( {x\,dy - y\,dx} \right)\sin \left( {{y \over x}} \right)$$

Which of the following is the solution of the above equation ($$C$$ is an arbitrary constant)

A
$${x \over y}\cos {y \over x} = C$$
B
$${x \over y}\sin {y \over x} = C$$
C
$$xy\,\cos {y \over x} = C$$
D
$$xy\,\sin {y \over x} = C$$
4
GATE CE 2014 Set 2
Numerical
+2
-0
Water is following at a steady rate through a homogeneous and saturated horizontal soil strip of $$10$$m length. The strip is being subjected to a constant water head $$(H)$$ of $$5$$m at the beginning and $$1$$m at the end. If the governing equation of flow in the soil strip is $$\,\,{{{d^2}H} \over {d{x^2}}} = 0\,\,$$ (where $$x$$ is the distance along the soil strip), the value of $$H$$ (in m) at the middle of the strip is _______.
GATE CE Subjects
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude
EXAM MAP
Joint Entrance Examination