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Solving higher derivatives equation

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sky_tm

Junior Member level 1
Higher Derivatives

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

Solve.

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)

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 ?

Re: Higher Derivatives

sky_tm said:
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.

Higher Derivatives

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

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