1
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
$$y = 36.95{e^{ - 2x}}$$
2
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
$$y = {C_1}\,{e^{ - 3x}} + {C_2}\,{e^{ - 2x}}$$
3
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
$$y = {e^{{{{x^3}} \over 3}}}$$
4
GATE CE 2005
+2
-0.6
Transformation to linear form by substituting $$v = {y^{1 - n}}$$ of the equation $${{dy} \over {dt}} + p\left( t \right)y = q\left( t \right){y^n},\,\,n > 0$$ will be
A
$${{dv} \over {dt}} + \left( {1 - n} \right)pv = \left( {1 - n} \right)q$$
B
$${{dv} \over {dt}} + \left( {1 + n} \right)pv = \left( {1 + n} \right)q$$
C
$${{dv} \over {dt}} + \left( {1 + n} \right)pv = \left( {1 - n} \right)q$$
D
$${{dv} \over {dt}} + \left( {1 - n} \right)pv = \left( {1 + n} \right)q$$
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
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