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
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Joint Entrance Examination