Solving higher derivatives equation

[sky_tm]

Higher Derivatives

\[\frac{{d^3 y}}{{dx^3 }} - 4\frac{{d^2 y}}{{dx^2 }} + 16\frac{{dy}}{{dx}} = 0\]

Solve.

 

[Hughes]

Re: Higher Derivatives

λ³-4λ²+16λ=0
λ1 = 0, λ2 = 2+4\[\sqrt 3\]i, λ3 = 2-4\[\sqrt 3\]i

y = C1 + C2 exp(2x) cos(4\[\sqrt 3\]x) + C3 exp(2x) sin(4\[\sqrt 3\]x)

 

[sky_tm]

Re: Higher Derivatives

thanks for the ans. but its different from mine... so can you help me find out what went wrong?

\[\lambda = 0\]
\[\lambda = 2 + 2j\sqrt 3\]
\[\lambda = 2 - 2j\sqrt 3\]

and btw how u got the exp, C1 C2 C3 ?

 

[Hughes]

Re: Higher Derivatives

thanks for the ans. but its different from mine... so can you help me find out what went wrong?

\[\lambda = 0\]
\[\lambda = 2 + 2j\sqrt 3\]
\[\lambda = 2 - 2j\sqrt 3\]

and btw how u got the exp, C1 C2 C3 ?

Sorry, it's my mistake. It should be 2 other than 4.

As for exp, you can consider it a formula.

C1, C2, C3 are arbitary consts.

 

[dreamcard]

Higher Derivatives

this can also be solved by using Laplace transformation. the zero input response of the equation