1
GATE ME 2005
+1
-0.3
If $${x^2}\left( {{{d\,y} \over {d\,x}}} \right) + 2xy = {{2\ln x} \over x}$$ and $$y(1)=0$$ then what is $$y(e)$$?
A
$$e$$
B
$$1$$
C
$${{1 \over e}}$$
D
$${{1 \over {{e^2}}}}$$
2
GATE ME 2003
+1
-0.3
The solution of the differential equation $${{dy} \over {dx}} + {y^2} = 0$$ is
A
$$y = {1 \over {x + c}}$$
B
$$y = - {{{x^3}} \over 3} + c$$
C
$$c\,\,{e^x}$$
D
unsolvable as equation is non-linear
3
GATE ME 1999
+1
-0.3
The equation $$\,\,\,{{{d^2}u} \over {d{x^2}}} + \left( {{x^2} + 4x} \right){{dy} \over {dx}} + y = {x^8} - 8\,\,{u \over {{x^2}}} = 8.\,\,\,$$ is a
A
partial differential equation
B
non-linear differential equation
C
non-homogeneous differential equation
D
ordinary differential equation
4
GATE ME 1998
+1
-0.3
The general solution of the differential equation $${x^2}{{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} + y = 0$$ is
A
$$Ax + B{x^2}$$ ($$A, B$$ are constants)
B
$$Ax + B\log x$$ ($$A, B$$ are constants)
C
$$Ax + B{x^2}\log x$$ ($$A, B$$ are constants)
D
$$Ax + Bx\log x$$ ($$A, B$$ are constants)
GATE ME Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
EXAM MAP
Joint Entrance Examination