need help solving this differential equation
2y^(4)+3y^(3)-16y" +15y'-4y=0

find general solution and particular
y(0)=-2, y'(0)=0, y"(0)=1, y^(3) (0)=1

Question

need help solving this differential equation 
2y^(4)+3y^(3)-16y" +15y'-4y=0

find general solution and particular 
y(0)=-2, y'(0)=0, y"(0)=1, y^(3) (0)=1

anonymous · Answer

using sythetic division 

I got  (x+4) as my first root resulting in 2x^3-5x^2+4x-1
I got (x+1) as my second root  resulting in 2x^2-3x +1 
now i am not sure what to do

john_es · Answer

You should solve the second degree equation. The factorized polynomial is,
$$2(x+4)(x-1)^2(x-1/2)$$
So, the general solution is,
$$y(x)=C_1e^{x/2}+C_2e^{-4x}+C_3e^{x}+C_4xe^{x}$$

john_es · Answer

You can obtain the value of the constants making the adecuate replacements.

anonymous · Answer

oh ok

anonymous · Answer

thats right you dont have to find the otherside because its zero

anonymous · Answer

got it