1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
solmaris [256]
3 years ago
6

Find the solution of the problem (1 3. (2 cos x - y sin x)dx + (cos x + sin y)dy=0.

Mathematics
1 answer:
lakkis [162]3 years ago
7 0

Answer:

2*sin(x)+y*cos(x)-cos(y)=C_1

Step-by-step explanation:

Let:

P(x,y)=2*cos(x)-y*sin(x)

Q(x,y)=cos(x)+sin(y)

This is an exact differential equation because:

\frac{\partial P(x,y)}{\partial y} =-sin(x)

\frac{\partial Q(x,y)}{\partial x}=-sin(x)

With this in mind let's define f(x,y) such that:

\frac{\partial f(x,y)}{\partial x}=P(x,y)

and

\frac{\partial f(x,y)}{\partial y}=Q(x,y)

So, the solution will be given by f(x,y)=C1, C1=arbitrary constant

Now, integrate \frac{\partial f(x,y)}{\partial x} with respect to x in order to find f(x,y)

f(x,y)=\int\  2*cos(x)-y*sin(x)\, dx =2*sin(x)+y*cos(x)+g(y)

where g(y) is an arbitrary function of y

Let's differentiate f(x,y) with respect to y in order to find g(y):

\frac{\partial f(x,y)}{\partial y}=\frac{\partial }{\partial y} (2*sin(x)+y*cos(x)+g(y))=cos(x)+\frac{dg(y)}{dy}

Now, let's replace the previous result into \frac{\partial f(x,y)}{\partial y}=Q(x,y) :

cos(x)+\frac{dg(y)}{dy}=cos(x)+sin(y)

Solving for \frac{dg(y)}{dy}

\frac{dg(y)}{dy}=sin(y)

Integrating both sides with respect to y:

g(y)=\int\ sin(y)  \, dy =-cos(y)

Replacing this result into f(x,y)

f(x,y)=2*sin(x)+y*cos(x)-cos(y)

Finally the solution is f(x,y)=C1 :

2*sin(x)+y*cos(x)-cos(y)=C_1

You might be interested in
What is the value of f(x)=2•2^x for f(-2)
Zigmanuir [339]

Answer:

The value of f(-2) is 1/2 or it can be written as 0.5.

Step-by-step explanation:

The given function is

f(x)=2\cdot 2^x

We have to find the value of f(-2).

Substitute x=-2 in the given function to find the value of f(-2).

f(-2)=2\cdot 2^(-2)

f(-2)=2\cdot \frac{1}{2^(2)}

f(-2)=\frac{1}{2}

f(-2)=0.5

Therefore the value of f(-2) is 1/2 or it can be written as 0.5.

3 0
3 years ago
What is the domain of the function 1x)= 2
Gnesinka [82]

Answer:

According to me, the answer is

Step-by-step explanation:

all real numbers

6 0
2 years ago
A picture representing 24÷6
Licemer1 [7]

Answer:

4

Step-by-step explanation:

24÷6

6 x ? = 24

6 goes into 24 four times

24÷6=4




7 0
2 years ago
Read 2 more answers
Write the equation of each ellipse in standard form with the given characteristics.
Eddi Din [679]

Answer:

Step-by-step explanation:

The foci are horizontally aligned.

horizontal ellipse:

(x-h)²/a² + (y-k)²/b² = 1

center (h,k)

vertices (h±a,k)

length of minor axis = 2b

foci (h±c,k), c² = a²-b²

Apply your data and solve for h, k, a, and b.

foci (±3√19, 6)

h = 0

k = 6

Length of minor axis = 2b = 10

b = 5

foci (h±3√19, 6)

c = 3√19

c³ = a² - b²

171 = a² - 25

a²  = 196

x²/196 + (y-6)²/25 = 1

6 0
2 years ago
What does -m+8=4m-7<br>equal <br>​
Olegator [25]

Answer:

3

Step-by-step explanation:

-m+8=4m-7

8=4m-(-m)-7

8=4m+m-7

8=5m-7

5m=8+7

5m=15

m=15/5

m=3

5 0
3 years ago
Read 2 more answers
Other questions:
  • The graph of a polynomial function is shown here.
    6·1 answer
  • There are 10 less red skittles than orange skittles in the bag. The orange skittles are also twice the number of red skittles. F
    15·2 answers
  • Constant of proportionality definition math is fun
    14·1 answer
  • Sarah earns $525 more than Andrew each month. They spend $1250 a month and save the rest. Sarah does not have any savings at fir
    9·1 answer
  • Please hurry I will mark you brainliest
    13·1 answer
  • Conjugate/Rational Number?
    14·1 answer
  • A suspension bridge spans a river 1350 ft. wide. 30% of the bridge is on one side of the river and 25% is on the other side. The
    5·1 answer
  • Write 0.1 x 0.1 x 0.1 x 0.1 using exponents
    5·2 answers
  • Please calculate this limit <br>please help me​
    15·1 answer
  • A triangle has sides of length 2 cm and 12 cm. What can you say about the length of the third​ side?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!