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
EXAM MAP
Medical
NEET