Page 120 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

215. Which ONE of the following is a (a) sec y + 2 sec y  tan y
linear non-homogeneous differential
equation, where x and y are the (b) tan y + 2 sec y  tan y
independent and dependent variables
respectively? 1
(c) sec y + 2 sec y 

dy − dy tan y
x
(a) + xy = e (b) + xy = 0
dx dx 1
(d) 2 [GATE]
dy − dy − tan y + sec y  tan y
y
(c) + xy = e (d) + e y = 0
dx dx 219. The solution of the differential
equation
[GATE-2014-EC-SET 3] ( x + y + 2x dx + 2ydy =
)
2
2
0
216. The integrating factor for the
differential equation (a) ( 2 y 2 ) = c
e x −
x
dp + K p = K L e − K t
1
dt 2 1 0 is (b) ( 2 y 2 ) = c
e x +
x
(a) e − K t (b) e − K t (c) ( 2 2 )
2
1
−
x
e x + y = c
(c) e K t (d) e K t
2
1
(d) ( x − 2 y 2 ) = c
−
x
e
[GATE-2014-CE-SET 2]
2
217. Consider the differential equation 220. Consider d y + b dy + cy = 0 where
( t − 81 ) dy + 5ty = sin ( ) t with dx 2 dx
2
dt b & c are real constants. If

y ( ) 1 = 2 . There exists a unique y = x e − 5x is a solution then
solution for this differential equation (a) both b and c are positive
when t belongs to the interval (b) b is positive, and c is negative

(a) (-2, 2) (b) (-10, 10) (c) b is negative but c is positive

(c) (-10, 2) (d) (0, 10) (d) both b and c are negative

[GATE-2017 EE SESSION-1] 221. The differential equation y + 11 y = 0
is subjected to the conditions
218. The integrating factor of
y ( ) 0 = , ( ) 0y  = . In order that
0
2
(cos sin 2y ) x dx + ( cos y − cos 2 ) x dy = 0
the equation has non-trivial solutions
is
the general value of  is

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