1
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
$${e^{ - x}}\sin \left( {{{\pi x} \over 2}} \right)$$
2
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
$$1.13$$
3
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
$$p=4, q=4$$
4
GATE ME 2005
+2
-0.6
Which of the following is a solution of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + \left( {q + 1} \right)y = 0?$$ Where $$p=4, q=3$$
A
$${e^{ - 3x}}$$
B
$$x{e^{ - x}}$$
C
$$x$$ $${e^{ - 2x}}$$
D
$${x^2}\,{e^{ - 2x}}$$
GATE ME Subjects
EXAM MAP
Medical
NEET