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beks73 [17]
3 years ago
13

Answer the questions below please

Mathematics
1 answer:
gavmur [86]3 years ago
4 0

Answer: For question #1, it’s #3. For question #2 a) it’s –12/5, for question #2 b, c and d) uh, let someone else can answer the rest of the question.

Step-by-step explanation: I solve the problem by solving this equation below.

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Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).
Firdavs [7]

Answer:

A) Particular solution:

2x+\frac{1}{2}e^{-x}-\frac{8}{5}

B) Homogeneous solution:

y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))

C) The most general solution is

y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}

Step-by-step explanation:

Given non homogeneous ODE is

y''+4y'+5y=10x+e^{-x}---(1)

To find homogeneous solution:

D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)

To find particular solution:

y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\

Substituting y_{p},y'_{p},y''_{p} in (1)

y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\

Equating the coefficients

5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\

The general solution is

y=y_{h}+y_{p}

from (2) ad (3)

y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}

6 0
3 years ago
What’s the diameter of a circle 5in
Molodets [167]

Answer:

About 1.591 in

Step-by-step explanation:

3 0
3 years ago
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EVERYONE, PLEASE HELP I NEED THIS DONE
zimovet [89]

Answer:

\frac{4}{5}

Step-by-step explanation:

\frac{32}{40}

Both 32 and 40 are divisible by 8.
32÷8=4

40÷8=5

Thus, the simplest form is \frac{4}{5}

7 0
2 years ago
Read 2 more answers
When converted to a household measurement, 9 kilograms is approximately equal to a
kondaur [170]

Answer:

9 kilograms is = 9000 grams

9 kilograms=317.466 ounces

Step-by-step explanation:

4 0
2 years ago
How many solutions?
Semmy [17]

Answer: A Single Solution

Step-by-step explanation:

7 0
3 years ago
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