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 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 $x^2y = 1 + cx$
Solution 03 $x^2y = 1 + cx$ → equation (1)
$x^2~dy + 2xy~dx = c~dx$
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)
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