1
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
$${{dv} \over {dt}} + \left( {1 - n} \right)pv = \left( {1 + n} \right)q$$
2
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
$${e^{ - 4x}}\left[ {\cos \,4x - {1 \over 4}\sin \,4x} \right]$$
3
GATE CE 2004
+2
-0.6
Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equation $$\,{{d\,x} \over {dt}} + k\,{x^2} = 0,$$ where $$k$$ is the reaction rate constant. If $$x=a$$ at $$t=0$$ then solution of the equation is
A
$$x = a\,{e^{ - kt}}$$
B
$$\,{1 \over x} = {\raise0.5ex\hbox{1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{a}} + k\,t$$
C
$$x = a\left( {1 - {e^{ - kt}}} \right)$$
D
$$x = a\, + k\,t$$
4
GATE CE 2001
+2
-0.6
The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \right) = - 3$$ is where $${{{d^2}y} \over {d{x^2}}} = 3x - 2$$
A
$$y = {{{x^3}} \over 3} - {{{x^2}} \over 2} = 3x - 2$$
B
$$y = 3{x^3} - {{{x^2}} \over 2} - 5x + 2$$
C
$$y = {{{x^3}} \over 2} - {x^2} - 5{x \over 2} + 2$$
D
$$y = {x^3} - {{{x^2}} \over 2} + 5x + {3 \over 2}$$
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