Question

Find the general solution for differential equation

(D4 - 5D3 + 5D2 + 5D - 6)y = 0
@Kevin Next Q

Answer 1

Question closed. Ready?

Answer 2

So we should find D value?

Answer 3

Dengan kata lain....
Menemukan solusi umum untuk persamaan diferensial

(D4 - 5 d 3 + 5 D 2 + 5 D - 6) y = 0

Answer 4

:D My Indonesian is kind of rusty...

Answer 5

Okay I try
(D4 - 5D3 + 5D2 + 5D - 6)y = 0

We have
(D4 - 5D3 + 5D2 + 5D - 6) = 0

and
y = 0

For
(D^4 - 5D^3 + 5D^2 + 5D - 6) = 0

(d+1)(d−1)(d−2)(d−3)=0
d+1=0 or d−1=0 or d−2=0 or d−3=0
d=−1 or d=1 or d=2 or d=3

Answer 6

:D my solution:

Given differential equation, (D4 - 5D3 + 5D2 + 5D - 6)y = 0

=> For general solution of equation,

Solve D4 - 5D3 + 5D2 + 5D - 6 = 0

=> D4 - 5D3 + 6D2 - D2 + 5D - 6 = 0

=> D2 (D2 - 5D + 6) - (D2 - 5D + 6) = 0

=> (D2 - 5D + 6)(D2 - 1) = 0 ................................(1)

Now

D2 - 1 = (D - 1)(D + 1) and

Factors of D2 - 5D + 6

D2 - 5D + 6 = D2 - 2D - 3D + 6

= D(D - 2) - 3(D - 2)

= (D - 3)(D - 2)

Therefore, equation (1) implies

(D2 - 5D + 6)(D2 - 1) = (D - 3)(D - 2)(D - 1)(D + 1) = 0

=> D = 3, 2, 1, -1 or D = -1, 1,, 2, 3

=> General solution of differential equation is,

=> y = C1 e-x + C2 ex + C3 e2x + C4 e3x .

Answer 7

Your Indonesian is good :D

Answer 8

So that's the answer :o

Answer 9

Alright I'm wrong XD
Go to another question again.
It's very fun

Answer 10

Oh YAY! : D