1
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 _______.
2
GATE CE 2012
+2
-0.6
The solution of the ordinary differential equation $${{dy} \over {dx}} + 2y = 0$$ for the boundary condition, $$y=5$$ at $$x=1$$ is
A
$$y = {e^{ - 2x}}$$
B
$$y = 2{e^{ - 2x}}$$
C
$$y = 10.95{e^{ - 2x}}$$
D
$$y = 36.95{e^{ - 2x}}$$
3
GATE CE 2010
+2
-0.6
The solution to the ordinary differential equation $${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} - 6y = 0\,\,\,$$ is
A
$$y = {C_1}\,{e^{3x}} + {C_2}\,{e^{ - 2x}}$$
B
$$y = {C_1}\,{e^{3x}} + {C_2}\,{e^{2x}}$$
C
$$y = {C_1}\,{e^{ - 3x}} + {C_2}\,{e^{2x}}$$
D
$$y = {C_1}\,{e^{ - 3x}} + {C_2}\,{e^{ - 2x}}$$
4
GATE CE 2007
+2
-0.6
The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x=0$$ is
A
$$y = {e^{{1 \over {2x}}}}$$
B
$$\ln \left( y \right) = {{{x^3}} \over 3} + 4$$
C
$$\ln \left( y \right) = {{{x^2}} \over 2}$$
D
$$y = {e^{{{{x^3}} \over 3}}}$$
EXAM MAP
Medical
NEET