1
GATE ME 2013
+2
-0.6
The solution to the differential equation $$\,{{{d^2}u} \over {d{x^2}}} - k{{du} \over {dx}} = 0\,\,\,$$ where $$'k'$$ is a constant, subjected to the boundary conditions $$\,\,u\left( 0 \right) = 0\,\,$$ and $$\,\,\,u\left( L \right) = U,\,\,$$ is
A
$$u = U{x \over L}$$
B
$$u = U\left( {{{1 - {e^{kx}}} \over {1 - {e^{kL}}}}} \right)$$
C
$$u = U\left( {{{1 - {e^{ - kx}}} \over {1 - {e^{ - kL}}}}} \right)$$
D
$$u = U\left( {{{1 + {e^{kx}}} \over {1 + {e^{kL}}}}} \right)$$
2
GATE ME 2012
+2
-0.6
Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ and $$\,\,y\left( 1 \right) = 1.\,\,\,$$ The complete solution of the differential equation is
A
$${x^2}$$
B
$$\sin \left( {{{\pi x} \over 2}} \right)$$
C
$${e^x}\sin \left( {{{\pi x} \over 2}} \right)$$
D
$${e^{ - x}}\sin \left( {{{\pi x} \over 2}} \right)$$
3
GATE ME 2008
+2
-0.6
It is given that $$y'' + 2y' + y = 0,\,\,\,\,y\left( 0 \right) = 0,y\left( 1 \right) = 0.$$ What is $$y(0.5)$$?
A
$$0$$
B
$$0.37$$
C
$$0.62$$
D
$$1.13$$
4
GATE ME 2005
+2
-0.6
The complete solution of the ordinary differential equation $${{{d^2}y} \over {d\,{x^2}}} + p{{dy} \over {dx}} + qy = 0$$ is $$\,y = {c_1}\,{e^{ - x}} + {C_2}\,{e^{ - 3x}}\,\,$$ then $$p$$ and $$q$$ are
A
$$p=3, q=3$$
B
$$p=3, q=4$$
C
$$p=4, q=3$$
D
$$p=4, q=4$$
GATE ME Subjects
EXAM MAP
Medical
NEET