arbitrary constants

Problem 06 | Elimination of Arbitrary Constants

Problem 6
Eliminate the c1 and c2 from x = c1 cos ωt + c2 sin ωt. ω being a parameter not to be eliminated.
 

Problem 05 | Elimination of Arbitrary Constants

Problem 5
Eliminate A and B from x = A sin (ωt + B). ω being a parameter not to be eliminated.
 

Problem 04 | Elimination of Arbitrary Constants

Problem 04
$cy^2 = x^2 + y$
 

Problem 04
$cy^2 = x^2 + y$       → equation (1)

$2cy~dy = 2x~dx + dy$

$c = \dfrac{2x~dx + dy}{2y~dy}$
 

Problem 03 | Elimination of Arbitrary Constants

Problem 03
$x^2y = 1 + cx$
 

Solution 03
$x^2y = 1 + cx$       → equation (1)

$x^2~dy + 2xy~dx = c~dx$
 

Problem 02 | Elimination of Arbitrary Constants

Problem 02
$y \sin x - xy^2 = c$
 

Solution 02

Elimination of Arbitrary Constants

Properties

  • The order of differential equation is equal to the number of arbitrary constants in the given relation.
  • The differential equation is consistent with the relation.
  • The differential equation is free from arbitrary constants.

Example
Eliminate the arbitrary constants c1 and c2 from the relation   $y = c_1 e^{-3x} + c_2 e^{2x}$.
 

Solution

 
 
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