Page 113 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

176. The partial differential equation 181. The degree of the differential
 2 u  2 u   2  2 1/4 3
2
xy − ( x − y 2 ) −    d y    d y
 x 2   equation y +  x   dx 2    = dx 3
x y
 2 u  u  u      
2
xy + y − x = ( 2 x − y 2 ) is.
 y 2  x  y
is 182. Match each of the items A, B, C with
an appropriate item from 1, 2, 3, 4
(a) Elliptic (b) Hyperbolic and 5

(c) Parabolic (d) None d y dy
2
(A) a 1  a y  a y = a
3
2
4
177. The partial differential equation dx 2 dx
 2 u + 4  2 u + 4  2 u = d y
3
 x 2    y 2 0 is (B) a 1 dx 3  a y = 2 a
x y
3
(a) Elliptic (b) Hyperbolic d y dy
3
2
(C) a 1 2  a x + a x y = 0
2
3
(c) Parabolic (d) None dx dx
178. The partial differential equation (1) non-linear differential equation
 2 u +  2 u −  2 u = (2) linear differential equation with

 x 2  y 2 z  2 0 is constant coefficients
(3) linear homogeneous differential
(a) Elliptic (b) Hyperbolic equation

(c) Parabolic (d) None (4) non-linear homogeneous
differential equation
179. One dimensional heat equation
 u =  2 u is (5) non-linear first order differential
t   x 2 equation
(a) A – 1, B – 2, C – 3
(a) Elliptic (b) Hyperbolic
(b) A – 3, B – 4, C – 2
(c) Parabolic (d) None
(c) A – 2, B – 4, C – 3
180. The two dimensional heal equation (d) A – 3, B – 1, C – 2
 2 u +  2 u =
 x 2  y 2 0 is [GATE-1994 (EC)]

183. The differential equation
(a) Elliptic (b) Hyperbolic 5
)
3
11
y + ( y 3 sin x y + = cos x is
1
y
(c) Parabolic (d) None

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