Page 95 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

60. The solution to 6yy − 1 25x = 0 (c) Both II and IV are true

represents a (d) Both III and IV are true

(a) family of circles [GATE-2017-EC-SECTION-1]
(b) family of ellipses
63. Which one of the following is the
(c) family of parabolas general solution of the first order
(d) family of hyperbolas differential equation

[GATE-2015 (PI)] dy
2
y
= (x + − ) 1 , where x, y are
di dx
61. A differential equation − 0.2i = 0 real?
dt
is applicable over 10 t  10. (a) y = + + tan − 1 (x c , where c

−
)
+
1 x
i −
i ( ) 4 = 10 , then ( ) 5 is _______.
is a constant
[GATE-2015-EE-SET-2]
)
+
1 x
(b) y = + + tan (x c , where c is
62. Consider the following statements a constant
about the linear dependence of the
)
+
1 x
real valued functions y = 1, y = (c) y = − + tan − 1 (x c , where c
x
1
2
and y = x , over the field of real is a constant
2
3
)
numbers. (d) y = − + tan (x c , where c is
+
1 x
I. y , y and y are linearly a constant
2
3
1
independent on 1 x−   0 [GATE-2017-EC-SECTION-1]
II. y , y and y are linearly 64. Consider the differential equation
1
3
2
dependent on 0 x  1 dy

(t − 81 ) + 5ty = sin ( ) t with
2
III. y , y and y are linearly y ( ) 1 = dt
2
1
3
dependent on 0 x  1 2 . There exists a unique
solution for this differential equation
IV. y , y and y are linearly when t belongs to the interval
1 2 3
independent on 1 x−   1
)
−
(a) ( 2,2 (b) ( 10,10− )
Which on among the following is
)
correct? (c) ( 10,2− ) (d) (0,10
(a) Both I and IV are true [GATE-2017-EE-SECTION-1]
(b) Both I and III are true

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