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3 years ago

Let y = y1(t) be a solution of y' + p(t)y = 0 (1)

Mathematics

1 answer:

murzikaleks [220]3 years ago

8 0

Answer:

a) See proof below

b)The result does not violate uniqueness of solutions.

Step-by-step explanation:

Suppose $y_1(t)$ is a solution of

$y'+p(t)y=0$

then

$y'_1+p(t)y_1=0$

If $y_2(t)$ is a solution of

$y'+p(t)y=g(t)$

then

$y'_2+p(t)y_2=g(t)$

To show that $y_1+y_2$ is a solution of equation (2) we have to show that

$(y_1+y_2)'+p(t)(y_1+y_2)=g(t)$

But

$(y_1+y_2)'+p(t)(y_1+y_2)=(y'_1+y'_2)+(p(t)y_1+p(t)y_2)=(y'_1+p(t)y_1)+(y'_2+p(t)y_2)=0+g(t)=g(t)$

which is what we wanted to show.

The results of the above problem does not violate uniqueness of solutions, because the solution is unique for each specific given initial condition, but there are no initial conditions stated.

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navik [9.2K]

Answer:

Because i have no more information i assume you would like it to be solved.

x < -1 or -1/3 < x < 1

4 0

4 years ago

Please this is overdue

andre [41]

P=12

A=15

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3 0

3 years ago

Read 2 more answers

Solve 3x2+7x+1=0 using the quadratic formula.

NNADVOKAT [17]

Answer:

$x=\frac{-7+-\sqrt{37} }{6}$

Step-by-step explanation:

This (±) goes between the $-7$ and $\sqrt{37}$

$3x^{2} +7x+1=0$

$ax^{2} +bx+c$

$-b$ ± $\sqrt{b^2-4ac}$ /2a

$-7$ ± $\sqrt{(7)^2-4(3)(1)}$ /2(3)

$-7$ ± $\sqrt{49-12}$ /6

$-7$ ± $\sqrt{37}/6$

7 0

3 years ago

Sara has $50 in her wallet in $5 and $20 bills. Create a linear equation (with

77julia77 [94]

Answer:

0 $20 bills and 10 $5 bills

1 $20 bills and 6 $5 bills

2 $20 bills and 2 $5 bills

Step-by-step explanation:

Equations

Let's set:

x=number of $5 bills

y=number of $20 bills

The total amount Sara has is given by

5x+20y

And we know it's equal to $50, thus:

5x+20y=50

Dividing by 5

x+4y=10

We would need another condition to solve for x and y, but we can determine some combinations that solve the problem.

Solving for x:

x=10-4y

Since both x and y are integers and cannot be negative:

10-4y≥0

Swapping sides:

4y≤10

Dividing by 4:

y≤2.5

Thus, y can only have the values {0,1,2}

For y=0

x=10-4*0=10

x=10

For y=1

x=10-4*1=6

x=6

For y=2

x=10-4*2=2

x=2

Thus, the possible combinations are:

0 $20 bills and 10 $5 bills

1 $20 bills and 6 $5 bills

2 $20 bills and 2 $5 bills

4 0

3 years ago

Suppose you have entered 115-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is

Maksim231197 [3]

Answer:

The distance of the run was 27 miles and the distance of the bicycle race was 88 miles.

Step-by-step explanation:

Since I have entered 115-mile biathlon that consists of a run and a bicycle race, and during my run, my average velocity is 9 miles per hour, and during my bicycle race, my average velocity is 22 miles per hour , and I finish the race in 7 hours, to determine what is the distance of the run and what is the distance of the bicycle race, the following calculations must be performed:

7 x 22 + 0 x 9 = 154

5 x 22 + 2 x 9 = 128

4 x 22 + 3 x 9 = 115

Therefore, the distance of the run was 27 miles and the distance of the bicycle race was 88 miles.

3 0

3 years ago