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Dafna11 [192]
3 years ago
9

Find the general solution of the given higher-order differential equation. d3u dt3 + d2u dt2 − 2u = 0

Mathematics
1 answer:
STALIN [3.7K]3 years ago
6 0

\dfrac{\mathrm d^3u}{\mathrm dt^3}+\dfrac{\mathrm d^2u}{\mathrm dt^2}-2u=0

This ODE has characteristic equation

r^3+r^2-2=(r^3-r)+(r^2+r-2)=r(r^2-1)+(r+2)(r-1)

=(r(r+1)+(r+2))(r-1)=(r^2+2r+2)(r-1)=0

which has roots at r=1,-1\pm i. Then the characteristic solution to the ODE is

u(t)=C_1e^t+C_2e^{(-1+i)t}+C_3e^{(-1-i)t}

\implies\boxed{u(t)=C_1e^t+C_2e^{-t}\cos t+C_3e^{-t}\sin t}

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3 years ago
Forty five men can construct a road 210m long in 60 days. What length would be constructed by 72 men in 50 days assuming that al
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2 years ago
Write first three common multiple of 3 , 5 and 6​
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Answer:

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Step-by-step explanation:

6 0
2 years ago
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In a missile-testing program, one random variable of interest is the distance between the point at which the missile lands and t
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Step-by-step explanation:

From the given data

we observed that the missile testing program

Y1 and Y2 are variable, they are also independent

We are aware that

(Y_1)^2 and (Y_2)^2 have x^2 distribution with 1 degree of freedom

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F_v(v)=\frac{e^{-\frac{v}{2}}}2

Since we have to find the density formula

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Therefore,

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8 0
3 years ago
Which value is a solution of the equation 5-4x=-3?<br> A. 0<br> B. 2<br> C. -3<br> D. 1/4
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