# Elimination of Arbitrary Constant

## Eliminate the Arbitrary Constants

Submitted by mburn on October 23, 2022 - 10:05am

Please do leave a solution so I can study it, thank you!

Obtain the differential equation by eliminating the arbitrary constants.

1. Cxsiny+x^(2)y=Cy

2. y=Ae^(-3x)-Be^(2x)+Cx^3

3. Ay=e^(Bx^2)

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## Differential equation: Eliminate the arbitrary constant from $y=c_1e^{5x}+c_2x+c_3$

Submitted by Awing on September 17, 2019 - 10:00am

y=c1e^5x+c2x+c3

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## Differential Equation: Eliminate $C_1$, $C_2$, and $C_3$ from $y=C_1e^x+C_2e^{2x}+C_3e^{3x}$

Submitted by EngineerInTheMaking on September 3, 2017 - 5:02pm

How to eliminate arbitrary constants

y=C1e^x+C2e^2x+C3e^3x

thank you :)

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## Elimination of arbitrary constants: $y = Ae^{ax} \cos (bx) + Be^{ax} \sin (bx)$

Submitted by wackadoodle on July 6, 2016 - 8:41pm

Im having a difficulty solving this problem y = Ae^{ax}cos(bx)+Be^{ax}sin(bx) where a and b are parameters. Can anyone show me how to solve this ?

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## Differential Equation: Eliminate $c_1$ and $c_2$ from $y = c_1 e^x + c_2 xe^x$

Submitted by omrcsr on June 17, 2016 - 8:34pm

eliminate the arbitrary constant:

y=c_{1}e^{x} + c_{2}xe^{x}

y'=c_{1}e^{x} + c_{2}(xe^{x }+ e^{x})

y''=c_{1}e^{x} + c_{2}(xe^{x }+ 2e^{x})

by comparing eq.1 and eq,2 = eq,4

by comparing eq.2 and eq.3 = eq.5

by comparing eq.4 and eq.5 = y'' + 2y - 3y'

am i doing it right??

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