Elimination of Arbitrary Constant

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)

y=c1e^5x+c2x+c3

How to eliminate arbitrary constants
y=C1e^x+C2e^2x+C3e^3x

thank you :)

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

eliminate the arbitrary constant:

y=c₁e^x + c₂xe^x

y'=c₁e^x + c₂(xe^x + e^x)
y''=c₁e^x + c₂(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??