Page 128 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

262. The curve for which the area of the 266. In which of the following differential
triangle formed by the x-axis, the equation degree is not defined?
tangent lie at any point P and line OP 2
2
2
2
is equal to a is (a) d y + 3    dy      = x log d y
dx 2  dx  dx 2
a 2
2
−
(a) x cy= + (b) y = x cx  2  2  2 
y  d y    dy   2  d y 
(b)  dx 2  +  dx     = x sin  dx 2 




a 2 a 2     
=
=
(c) y cx + (d) x cy −  
x y  dy 
(c) x = sin  dx − 2y    , x  1
263. For the differential equation whose  
)
2
2
solution is (x h + ( y k ) = a   dy  
−
−
2
(d) x − 2y = log    
(a is a constant), its  dx 
(a) order is 2 (b) order is 3 267. y = ae − 1/ x + b is a solution of
(c) degree is 2 (d) degree is 3 dy = y , then
dx x 2
+
dy ax h
264. The solution of =
+
dx by k (a) a  R −   0
represents a parabola when
0
(b) b =
(a) a = 0, b  0 (b) a  0, b  0
(c) b = 1
(c) b = 0, a  0 (d) a = 0, b  R
(d) a takes finite number of values

265. The solution of the differential 268. Which of the following equation(s) is
equation ( x y − ) 1 dy + 2xy dx = / are linear?
2
2
3
0
is dy y
(a) + = log x
(a) 1 x y+ 2 2 = cx dx x
  dy  
+
(b) 1 x y = 2 2 cy (b) y   dx     + 4x = 0

0
(c) y =  dy 
(c) (2x + y 3 )       = 3y
1  dx 
(d) y = −
x 2 (d) None of these

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