Page 118 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

206. The solution of the differential 209. The solution of
equation dy =   + tan  
y
y
 
 

  
dx     x is
x
 
 
2
−
−
2
0
y 1 x dy + x 1 y dx = is
  y  
−
(a) 1 x = 2 c (a) sin    x    = xc
 y 
(b) 1 y− 2 = c (b) tan       = xc
 x 
−
2
−
2
(c) 1 x + 1 y =  y 
c
(c) cosec       = xc
+
2
(d) 1 x + 1 y =    x 
2
+
c
(d) cot    y    = xc
[ESE-2017 (EE)]  x 
207. The figure shows the plot of y as a 210. Solve the differential equation,
function of x. The function shown is 2 dy 3 3
the solution of the differential xy dx = x + y
equation (assuming all initial
conditions to be zero) is [GATE-1994-ME]
2
d y dy 211. A curve passes through the point (x =
(a) = 1 (b) = + x 1, y = 0) and satisfies the differential
dx 2 dx
2
dy dy dy = x + y 2 + y
(c) = − x (d) = x equation dx 2y x . The
dx dx
equation that describes the curve is
[GATE-2014 (IN-SET 1)]
  y 2  

HOMOGENEOUS DIFFERENTIAL (a) ln 1+ 2   = x − 1

EQUATION  x 

dy 1   y 2  
208. The solution of = sin (x + ) y is (b) ln 1+  = x − 1

dx 2   x 2  
(
) sec x +
x c
(a) tan x + y − ( ) y = +  y 

(c) ln 1+ x     = x − 1

2
(
(b) sec x + y ) tan x− ( + ) y = x + c  
2
1   y  
(

+
(c) tan x + y ) cos x− ( + ) y = x c (d) ln 1+ x     = x − 1
2

(
+
(d) tan x + y ) cot x− ( + ) y = x c
[GATE 2018 (EC)]

116