Page 113 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes Differentiation (1) w.r.t. x, we get
dy x  2x
 A e  2Be ...(2)
dx
Differentiating (2) again, we get

2
d y x  2x
 A e  4Be
2
dx
 2
Be
  Ae  x 2Be  2x   Ae x   2x 
dy
=   2y from (1) and (2).
dx
Thus, the required differential equation is
2
d y dy
y
  2  0.
2
dx dx
Example: Form the differential equation of simple harmonic motion given by x = A
cos(nt + B)
Solution:

The given equation is x = A cos(nt + B) ...(1)
Differentiating (1) with respect to ‘t’, we get

dx
  Asin(nt  B).n ...(2)
dt
Differentiating (2) again with respect to ‘t’, we have

2
d x 2 2
  A cos(nt  B).n   An cos(nt  B)
dt 2
 n2x, from (1)

2
d x 2
or,  n x  0 is the required differential equation.
dt 2

~1
~1
Example: Form the differential equation from the relation sin x + sin y = C
Solution:
~1
~1
Given sin x + sin y = C
Differentiating (1) w.r.t. ‘x’, we have
1 1 dy
  0
1 x 2 1 y 2 dx

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