Page 123 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

x
x
(3) e − x cos10x + 0.1e 235. Consider y − 11 y = 2e if y(0) = 0,
0
y 1 ( ) 0 = then y(1) =
(a) P – 2, Q – 1, R – 3
(b) P – 1, Q – 3, R – 2 (a) e + sin h (1) (b) cos h(1)

(c) P – 1, Q – 2, R – 3 (c) sin h(1) (d) cos h(1) + 1

[CSIR]
(d) P – 3, Q – 2, R – 1
236. Suppose ( ) x = x cos2x is a
y
[GATE-2006 (IN)] p
particular integral of
11
233. The solution of the differential y +  y = − 4sin2x , then the
2
d y constant  is _____
equation k 2 = y − y under the
dx 2 2 [GATE]
boundary conditions
CAUCHY HOMOGENEOUS LINEAR
(i) y = y at x = 0 and DIFFERENTIAL EQUATIONS
1

(ii) y = y at x =  , where k, y and 237. The general solution of the
2
1
y are constants, is differential equation
2
2
d y − x dy + y =
2
x
exp −
(a) y = ( y − y 2 ) ( / x k 2 ) + y dx 2 dx 0 is:
1
2
2
(b) y = ( y − y 1 )exp − / ) y (a) Ax + Bx (A, B are constants)
( x k +
1
2
+
)
( /
(c) y = ( y − y 2 )sinh x k + y (b) Ax B log x (A, B are constants)
1
1
+
( x k +
(d) y = ( y − y 2 )exp − / ) y (c) Ax Bx 2 log x (A, B are
1
2
constants)
[GATE-2007-EC] (d) Ax Bx logx (A, B are
+
234. Consider the following second-order constants) [GATE-1998]
differential equation: 238. The radial displacement in a rotating
2
1
11
y − 4y + 3y = 2t − 3t . The disc is governed by the differential
particular solution of the differential d u 1 du u
2
equation is equation 2 + − 2 = 8x
dx x dx x
−
−
2
− −
(a) 2 2t t − 2 (b) 2t t where u is the displacement and x is
the radius. If u = 0 and x = 0, and u =
2
2
(c) 2t − 3t (d) 2 2t− − − 3t
[GATE-2017 CE SESSION-II]

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