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.
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Problem 6
Eliminate the c1 and c2 from x = c1 cos ωt + c2 sin ωt. ω being a parameter not to be eliminated.
Problem 5
Eliminate A and B from x = A sin (ωt + B). ω being a parameter not to be eliminated.
Problem 02
$y \sin x - xy^2 = c$
Solution 02
$(y \cos x~dx + \sin x~dy) - (2xy~dy + y^2~dx) = 0$
Problem 01
$x^3 - 3x^2y = c$
Solution 01
Properties
Example
Eliminate the arbitrary constants c1 and c2 from the relation $y = c_1 e^{-3x} + c_2 e^{2x}$.
Solution
$y' = -3c_1 e^{-3x} + 2c_2 e^{2x}$ → equation (2)
$y'' = 9c_1 e^{-3x} + 4c_2 e^{2x}$ → equation (3)