Mathematics High School

What do I do with e^y in the differential equation dy/dt =(2t)/(e^y)?

Answers

Answer 1

As you said, the equation is separable:

dy/dt = 2t / exp(y)

exp(y) dy = 2t dt

Integrate both sides:

∫ exp(y) dy = ∫ 2t dt

exp(y) + C₁ = t ² + C₂

Move the constant terms to one side. When you add them together, you get another constant, so you can ignore the subscript altogether:

exp(y) = t ² + C

Solve for y explicitly by taking the logarithm of both sides:

ln(exp(y)) = ln(t ² + C )

y = ln(t ² + C )

C can be any number; if it happens to be 0, then you have

y = ln(t ²) = 2 ln(t )

so B is the correct choice.

You can also approach this from the opposite angle: Assume y is one of the given solutions, then substitute it into the ODE. (Bit more trial-and-error involved, so not a good idea if you're short on time.)

For example, if y = 2 exp(t ) as in choice A, you have dy/dt = 2 exp(t ), so the ODE would become

2 exp(t ) = 2t / exp(2 exp(t ))

which is clearly (I hope) not true.

Related Questions

What is a No solution? What is a infinite solution?

Answers

No is a solid answer and infinite solution well that just means anything

Answer:

No solution would mean that there is no answer to the equation. ... Infinite solutions would mean that any value for the variable would make the equation true?

A refrigerator has a marked price of $5000. Mr. Jones bought it on hire purchase for $7500. What is the extra cost Mr. Jones paid as a percentage of the cash price? *

A) 66.6%
B) 33.3%
C) 50%
D) 75%

Answers

The answer is C. 50% because 50% of 5,000 is 2,500 and 2,500+5,000= 7,500

50% because the 50% of 5000 is 2500 and 5000+2500=7500

5+5 also i like people

Answers

Answer:

5+5=10 :D

Step-by-step explanation:

Answer:

huh

Step-by-step explanation:

Which is the following functions is graphed below?

Answers

Answer:

A.y=|x|+7

Step-by-step explanation:

your answer is A !!!!

Plz I need help ASAP

Answers

Answer:

Step-by-step explanation:

5.50p=5.50x4=22

I hope this is the answer you're looking for! :)

I just edited it.

Perform the following multiplication

a) 9xy ( x²y – xy²)

b) 7 p?q? (9 pq - 9 p²q²)

Answers

Answer:

a: (9x^3y^2)-(9x^2y^3)

Step-by-step explanation:

Help me please!!! Whats the length for w?

Answers

Answer:

(The second option) sin40° = w / 28

Step-by-step explanation:

sin40° = opposite / hypotenuse

sin40° = w / 28

Son=40 hope this helps

help quickly!!!!! explanation needed. lots of points.

Answers

Answer:

29.3

Step-by-step explanation:

to find average you find the sum of all the minutes she practiced and divide it by the total amount of day she practiced.

first we have to find the sum of the minutes she practiced:

20+30+40+38+25+22+39+22+26+31

this equation is equal to 293 minutes she practiced in total. Now we have to divide this by the total amount of days she practiced whice according to the data is 10! So:

293/10 =29.3

Can anyone help me choose the correct answer?!

Answers

Answer:

f(x)=9x-7

when x=-1

f(-1)=9×-1-7=-9-7=-16

when x=0

f(0)=9×0-7=-7

other are similar to this

Find the value of f(-8).

Answers

9514 1404 393

Answer:

Step-by-step explanation:

F(-8) is found by locating x = -8 on the x-axis, then determining the y-coordinate the graph has at that point.

f(-8) = 8

Select the correct answer from each drop-down menu.
Two sides of a right triangle measure 5 inches and 6 inches, and the third side measures V61 inches.
inches.
The length of the third side is about
inches. The perimeter of the triangle is about
Please help

Answers

Answer:

7.8 and 18.8 is your answer

Step-by-step explanation:

give other person brainliest and yes Ik I’m very late ~w~

two times the sum of a number and 18 is at least -21

Answers

Answer:

2x + 18 ≥ 21

x ≥ 2/3

Step-by-step explanation:

Let sum be X

2 times the sum means 2x

the sum of a number and 18 means x + 18

at least -21 means ≥ 21

put them together, and you get, 2x + 18 ≥ 21

If solving for x,

2x + 18 ≥ 21

2x ≥ 3

x ≥ 2/3

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Henry deposits $7500 in an account earning 2.75% interest compounded monthly. What is the balance in his account after 4 years?

A.$27,579.67
B.$20,160
C.$10,420.49
D.$8371.03

Answers

Answer:

Answer is D

Step-by-step explanation:

PLS HELP!!!! I dont understand this.

Answers

Answer:

a) 3m + m

b) 2m + 2m

Answer:

Step-by-step explanation:

a) 3m + m

b) 2m + 2m

Tom drives 200 miles in 4 hours.
He drives the first 32 miles at an average speed of 64 mph
Work out his average speed for the rest of the journey, in mph.
Please help??

Answers

His average speed for the rest of the journey was of 48mph.

if tom is driving 200 miles in 4 hours... and drives the first 32 miles in half an hour... his speed for the rest of the trip would most likely be 48 mph because 3.5 hours are left and 168 miles are left and when you divide that it comes out to 48.

A gym charges an initial fee plus $25 per month. John paid $200 for six months. Assume the relationship is linear.

a.What is the rate of change and what does it mean in context to the situation?
b. What is the initial value and what does it mean and context to the situation?

i will give brainliest!!!!!

Answers

Step-by-step explanation:

a. The rate of change is $33.33 per month

200/6 = approximately $33.33 per month

This means that in addition to the initial fee, Josh has to pay $33.33 per month for the gym membership.

b. The initial value is $25. This is a constant value and a one time fee to open and attain a gym membership.

PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP
Translate the sentence into an inequality.

Twice the difference of a number and 5 is at most 23.

Use the variable x for the unknown number.

Answers

Answer:

[tex] 2(x - 5)\leqslant \\23[/tex]

Step-by-step explanation:

[tex]2x - 10 \leqslant 23[/tex]

The price of a gallon of unleaded gas was 2.84 yesterday. Today, the price rose to 2.90 . Find the percentage increase. Round your answer to the nearest tenth of a percent.

Answers

Answer:
102.1%
Explanation: 2.90/2.84=1.021x100

(50Pts) When using the vertical method to multiply polynomials, your like terms must be lined up in ____________.

descending order
ascending order
columns
rows

Answers

I think you line them up in columns

Answer:

C. Columns

Step-by-step explanation:

It's correct, I took the test and got it right.

A sequence is given below.

576, 288, 144, 72, . . .

Answers

The answer would be 36

〖x/y^(-1) )〗^0 〖(x^(-1)/y^2 )〗^2 〖(xy^2)〗^(-1)
Exponent solving

Answers

Anything to the 0 power equals 1....

Erik used the Factor Theorem to find the remainder of 2x3-4x2-28x+6 divided by x+3. If he calculated the remainder to be 0, what does that tell him?

Answers

Step-by-step explanation:

x + 3 = 0

x = - 3

f(x) = 2x³ - 4x² - 28x + 6

f(- 3) = 2(- 3)³ - 4(- 3)² - 28 x (- 3) + 6

= 2 x (- 27) - (4 x 9) + 84 + 6

= - 54 - 36 + 90

= - 90 + 90

= 0

Therefore,

x + 3 is factor of 2x³ - 4x² - 28x + 6

5x + 13 + (2y-7)i = -2 + i please please help

Answers

hope this helps !!!!

Forty out of 50 people surveyed in a small towns' coffee shop are
planning on voting in the next election. If there are 400 people in the
town, how many people do you predict will vote in the next election? *

Answers

the amount of people voting in town next year would be 320

Identify the vertex for the graph of y = -2x2 - 12x +1. (1 point)
O (-3, 19)
0 (-3,55)
(3, -53)
(3, -47)

Answers

Answer:

(-3, 19)

Step-by-step explanation:

Monique bought 3 boxes of cereal at the grocery store. Each box of cereal costs c dollars. Which equation represents the total amount of money, t, Monique spent on cereal?

Answers

Answer:

3c = t

Step-by-step explanation:

3 cereal boxes is 3c and the total is t. so 3c = t

Answer:

3c = t

3 is the amount of boxes, c is the money, therefore, it is 3c=t, which means c times the number of boxes equals t

About 0.6 of all the students in the fifth grade are girls. If the fifth grade has 85 students, how many of the students are girls?

Answers

Answer:

51 girls

Step-by-step explanation:

85 represents the total amount of students in 5th grade, including boys and girls.

0.6 or 60% of the 85 students in 5th grade are girls.

0.6 x 85 = 51

Therefore, there are 51 girls out of the 85 students in 5th grade.

the answer is 51. hope i helped

A rectangle has sides measuring (2x + 5) units and (3x + 12) units.
Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. (6 points)
Part B: What is the degree of your answer from part A? What is the classification of your answer obtained in Part A ( monomial, binomial, trinomial, polynomial)? (4 points)

Answers

Answer:

Step-by-step explanation:

Area = (2x+5)( 3x+12) square units

= 6x² + 39x + 60 square units

Trinomial

I WILL GIVE BRAINLIEST!!

Answers

Answer:

[tex]\text{D. The terms may be combined.}[/tex]

Step-by-step explanation:

Recall that [tex]\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}[/tex]. Using this, we can simplify and combine the two terms:

[tex]6\sqrt{32}-12\sqrt{72},\\=6\cdot \sqrt{4}\cdot \sqrt{8}-12\cdot \sqrt{9}\cdot \sqrt{8},\\=6\cdot 2\cdot \sqrt{8}-12\cdot 3\cdot \sqrt{8},\\=12\sqrt{8}-36\sqrt{8},\\=-24\sqrt{8}=-24\cdot\sqrt{4}\cdot\sqrt{2}=\boxed{-48\sqrt{2}}[/tex]. Therefore, the terms may be combined.

statistics is a numerical value summarizing the sample date

true or false

Answers

True szzzzzzzzzzzzzzzzz

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