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

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

Chef Selena is making her special dish that requires pasta, sauce, and onions. She has 5 1/8 pounds of pasta, 6 pounds of sauce,

arlik [135]

Answer:

$\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}$

Step-by-step explanation:

The Weight of Ingredients to be used by Chef Selena are:

$5\frac{1}{8}$ pounds of pasta,
6 pounds of sauce; and
$4\frac{7}{8}$ pounds of onions.

Total Weight of Food Made, x

$=5\frac{1}{8}+6+4\frac{7}{8}\\=5+6+4+\frac{1}{8}+\frac{7}{8}\\=16 \: Pounds$

Since each serving is $\frac{1}{2} Pounds$

Number of Servings of her dish, y

$16 \div \frac{1}{2}\\ =32 \: Servings$

The two equations needed to solve the problem are therefore:

$\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}$

4 0

3 years ago

What is the GCF of 9h^3 - 12h

sattari [20]

It would be 3h(3h^2 -4), it is factored

5 0

4 years ago

To visit her grandmother, Jessica takes a horse 3.31 kilometers and a motorcycle 1 kilometer. How many kilometers is Jessica’s j

umka21 [38]

The total distance she travelled 4.1 Km.

<h3>What is unitary method?</h3>

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Jessica takes a horse 3.31 kilometers

Through a motorcycle she travel 1 kilometer.

So, the total distance travelled

=3.31 + 1

=4.31 Km

Hence, the total distance they travelled is 4.31 Km.

Learn more about unitary method here:

brainly.com/question/22056199

#SPJ2

8 0

1 year ago