Page 85 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

Differential Equations With real constant coefficients, then
the least possible value of n is
+
)) b
1. If y = ln (sin (x a + , where a
(a) 1 (b) 2
and b are constants, is the primitive,
then the corresponding lowest order (c) 3 (d) 4
differential equation is
[JAM CA 2011]
( ( ) 2 ) 4. The differential equation representing
11
1
(a) y = − 1+ y
the family of circles touching y-axis
at the origin is
2
1
y
(b) y = 11 y − 2 ( )
(a) Linear and of first order
2
1
y
(c) y = 11 1+ ( ) (b) Linear and of second order
2
(d) y = 11 y + 1 y [JAM CA 2005] (c) Non-linear and of first order
(d) Non-linear and of second order
2. Which one of the following
differential equations represent all [JAM MA 2006]
circles with radius a?
5. Solution of the differential equation
2
 dy  2 d y xy + 1 sin2y = x 3 sin y is
2
2
(a) 1+       + a − x 2 = 0
 dx  dx 2 (a) cot y = − x + cx
3
2
 dy  2 d y (b) 2cot y = x + 3 2cx
2
2
2
(b) 1+       + a − y 2 = 0
 dx  dx 2
2
3
(c) tan y = − x + cx
   dy  2  3  d y 2 3 2
2 

(c) 1+        + a 2   2    = 0 (d) 2tan y = x + 2cx
 dx    dx
       [JAM CA 2005]
   dy  2  3  d y 2 6. General solution of the differential
2 
(d) 1+         = a 2   2    − / y x
 dx    dx equation xdy = ( y + xe ) dx is
      
given by
[JAM CA 2008]
+
(a) e − / y x = ln x c
3. If y = x cosx is a solution of an nth
+
order linear differential equation (b) e / y x = ln x c
n
d y + a d n− 1 y + ...... a dy + a y = 0 (c) e − / x y = x c
+
+
dx n 1 dx n− 1 n− 1 dx n

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