1
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
$$y = {C_1}\,{e^{ - 3x}} + {C_2}\,{e^{ - 2x}}$$
2
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
$$y = {e^{{{{x^3}} \over 3}}}$$
3
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
$${{dv} \over {dt}} + \left( {1 - n} \right)pv = \left( {1 + n} \right)q$$
4
GATE CE 2005
+2
-0.6
The solution $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 17y = 0;$$ $$y\left( 0 \right) = 1,{\left( {{{d\,y} \over {d\,x}}} \right)_{x = {\raise0.5ex\hbox{\pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{4}}}} = 0\,\,$$ in the range $$0 < x < {\pi \over 4}$$ is given by
A
$${e^{ - x}}\left[ {\cos \,4x + {1 \over 4}\sin \,4x} \right]$$
B
$${e^x}\left[ {\cos \,4x - {1 \over 4}\sin \,4x} \right]$$
C
$${e^{ - 4x}}\left[ {\cos \,4x - {1 \over 4}\sin \,x} \right]$$
D
$${e^{ - 4x}}\left[ {\cos \,4x - {1 \over 4}\sin \,4x} \right]$$
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