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Gala2k [10]
3 years ago
10

Diff Eq dy/dx= (ycos(x))/(1+y^2) initial condition is y(0)=1 work below ...?

Mathematics
1 answer:
Volgvan3 years ago
5 0
Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2
You might be interested in
Indicate the answer choice that best completes the statement or answers
zysi [14]

Answer:

Option D. y = 5x + 1

Step-by-step explanation:

From the question given above, the following data were:

Input (x) >>>>>> Output (y)

0 >>>>>>>>>>>> 1

1 >>>>>>>>>>>> 6

2 >>>>>>>>>>>> 11

3 >>>>>>>>>>>> 16

4 >>>>>>>>>>>> 21

To know the the correct answer to the question, we shall apply the equation given in each option to see which will satisfy the table. This can be obtained as follow:

For Option a

y = 3x + 3

x = 0

y = 3(0) + 3

y = 0 + 3

y = 0

y = 3x + 3

x = 1

y = 3(1) + 3

y = 3 + 3

y = 6

For Option b

y = 5x – 4

x = 0

y = 5(0) – 4

y = 0 – 4

y = – 4

y = 5x – 4

x = 1

y = 5(1) – 4

y = 5 – 4

y = 1

For Option c

y = 10x – 9

x = 0

y = 10(0) – 9

y = 0 – 9

y = – 9

y = 10x – 9

x = 1

y = 10(1) – 9

y = 10 – 9

y = 1

For Option d

y = 5x + 1

x = 0

y = 5(0) + 1

y = 0 + 1

y = 1

y = 5x + 1

x = 1

y = 5(1) + 1

y = 5 + 1

y = 6

From the illustrations made above, only option d satisfy the table. Thus, option d gives the correct answer to the question.

5 0
3 years ago
Write the equation for the inverse function of y=0.4x-1.2
loris [4]
I think it is 0.4/0.4 but I'm not sure
7 0
3 years ago
Plz help me 25y−4+7−910y =
Elena-2011 [213]

Answer:

-885y+3

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Please helppp me I need it now
Aleksandr [31]

Answer:

You can either choose B or D.

8 0
2 years ago
Read 2 more answers
Use the distributive property to simplify the expression 6(s-9
Natalija [7]
You have to multiply the 6 by both s and -9

So you will get 6s - 54 which is the answer
7 0
2 years ago
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