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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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-(2x+5)=-10-2x plz help
Scilla [17]

−(2x+5)=−10−2x

Step 1: Simplify both sides of the equation.

−(2x+5)=−10−2x

−2x+−5=−10+−2x(Distribute)

−2x−5=−2x−10

Step 2: Add 2x to both sides.

−2x−5+2x=−2x−10+2x

−5=−10

Step 3: Add 5 to both sides.

−5+5=−10+5

0=−5

Answer:

There are no solutions.

4 0
3 years ago
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Ghella [55]
The correct answer is B.

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3 years ago
Determine whether the given linear equations are parallel, perpendicular, or neither.
ladessa [460]

Answer:

A. Perpendicular

Step-by-step explanation:

Lines are perpendicular if their slopes are opposite reciprocals of each other. Opposite, meaning if positive, the other slope is negative, and if negative, the other slope is positive. Reciprocal meaning, the number is flipped upside down, turning fractions into whole numbers and vice versa.

1/9  

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The slopes are perpendicular

4 0
3 years ago
4×3-(2×3-16÷4) the answer with work​
Reika [66]

Answer:

10

Step-by-step explanation:

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3 0
3 years ago
Read 2 more answers
4. Kristina is allowed to have a friend sleep over every 3rd weekend,
PSYCHO15rus [73]

Answer:

6

Step-by-step explanation:

You must find the least common multiple of their schedules.

The numbers 3 and 2 are their own prime factors, so the least common multiple of 3 and 2 is 6.

Six weekends must pass until they can both have someone over on the same night.

The number line below shows that the first time their sleepovers coincide is Week 6.

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