Page 94 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations
(
(a) 2cos 2x + ) 3 − sin (2x + ) 3 57. Consider the following differential
equation:
(
(b) 2sin 2x + ) 3 + cos (2x + ) 3 dy = − 5 ; initial condition: y = at
y
2
dt
(
(c) sin 2x + ) 3 − 2cos (2x + ) 3 t = 0
3
(
(d) 2sin 2x + ) 3 − cos (2x + ) 3 The value of y at t = is
−
(a) 5e − 10 (b) 2e − 10
[JAM GP 2009] −
−
2
(c) 2e 15 (d) 15e
2x
2x
55. If e and xe are particular [GATE-2015-ME-SET-2]
solutions of a second order 58. Consider the differential equation
homogeneous differential equation dx
−
with constant coefficients, then the dt = 10 0.2x with initial condition
equation is x ( ) 0 = 1. The response ( ) t for
x
t  0 is
2
d y dy
0
(a) − 4 + 4y = − 0.2t 0.2t
−
−
dx 2 dx (a) 2 e (b) 2 e
−
−
(c) 50 49e − 0.2t (d) 50 49e 0.2t
2
d y dy
(b) − 5 + 6y = 0 [GATE-2015-EC-SET-2]
dx 2 dx
59. Consider the following differential
equation:
2
d y
(c) − 4y = 0 y
dx 2 ( x ydx xdy )cos =
+
x
2
d y dy y
(d) − 3 + 2y = 0 ( y xdy − ydx )sin
dx 2 dx x
Which of the following is the solution
[JAM GP 2010] of the above equation (c is an
56. The general solution of the arbitrary constant)?
+
dy 1 cos2y x y
differential equation = (a) cos = c
−
dx 1 cos2x y x
is x y
(b) sin = c
=
(a) tan y − cot x c (c is a constant) y x y
=
(b) tan x − cot y c (c is a constant) (c) xy cos = c
x
=
(c) tan y + cot x c (c is a constant) (d) xy sin y = c
=
(d) tan x + cot y c (c is a constant) x
[GATE-2015-CE-SET-1]
[GATE-2015-EC-SET-2]

92