Please help Combine like terms. 9y + 5y

yawa3891 [41]

a) The solution of this ordinary differential equation is $y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }$ .

b) The integrating factor for the ordinary differential equation is $-\frac{1}{x}$ .

The particular solution of the ordinary differential equation is $y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$ .

<h3>How to solve ordinary differential equations</h3>

a) In this case we need to separate each variable ( $y, t$ ) in each side of the identity:

$6\cdot \frac{dy}{dt} = y^{4}\cdot \sin^{4} t$ (1)

$6\int {\frac{dy}{y^{4}} } = \int {\sin^{4}t} \, dt + C$

Where $C$ is the integration constant.

By table of integrals we find the solution for each integral:

$-\frac{2}{y^{3}} = \frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32} + C$

If we know that $x = 0$ and $y = 1$ , then the integration constant is $C = -2$ .

The solution of this ordinary differential equation is $y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }$ . $\blacksquare$

b) In this case we need to solve a first order ordinary differential equation of the following form:

$\frac{dy}{dx} + p(x) \cdot y = q(x)$ (2)

Where:

$p(x)$ - Integrating factor
$q(x)$ - Particular function

Hence, the ordinary differential equation is equivalent to this form:

$\frac{dy}{dx} -\frac{1}{x}\cdot y = x^{2}+\frac{1}{x}$ (3)

The integrating factor for the ordinary differential equation is $-\frac{1}{x}$ . $\blacksquare$

The solution for (2) is presented below:

$y = e^{-\int {p(x)} \, dx }\cdot \int {e^{\int {p(x)} \, dx }}\cdot q(x) \, dx + C$ (4)

Where $C$ is the integration constant.

If we know that $p(x) = -\frac{1}{x}$ and $q(x) = x^{2} + \frac{1}{x}$ , then the solution of the ordinary differential equation is:

$y = x \int {x^{-1}\cdot \left(x^{2}+\frac{1}{x} \right)} \, dx + C$

$y = x\int {x} \, dx + x\int\, dx + C$

$y = \frac{x^{3}}{2}+x^{2}+C$

If we know that $x = 1$ and $y = -1$ , then the particular solution is:

$y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$

The particular solution of the ordinary differential equation is $y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$ . $\blacksquare$

To learn more on ordinary differential equations, we kindly invite to check this verified question: brainly.com/question/25731911

3 0

2 years ago

9x-3y=27 -6x+9y=24 idek what this is but i need help

lbvjy [14]

Answer:

Step-by-step explanation:

if x=6 y=9 that is answer. I just know, but think. BOI

8 0

3 years ago

Can you please assist

ELEN [110]

A. (Number of sides - 2) x 100, so
6-2= 4 x 180
= 720° is the sum of all angles in a hexagon
84 + 87 + 128 + 150 + 103 = 552
720 - 552 = 168
X = 168°

2. Angles in a triangle sum up to 180°
36 + 57= 93
180 - 93 = 87
A= 87°

8 0

2 years ago

The length of a rectangle is 11 in. longer than its width. The perimeter of the rectangle is 86 in.

aliina [53]

Let the width = x then length = x + 11 inches

Perimeter of a rectangle = 2*width + 2*length so we have the equation:-

( letting P = perimeter , L = length and W = width)

P = 2L + 2W

86 = 2(x + 11)) + 2x

86 = 4x + 22

4x = 86-22 = 64

x = 64 / 4 = 16 inches

Therefore the length of the rectangle = 16 + x

= 16 + 11 = 27 inches Answer

4 0

2 years ago

Read 2 more answers

Help please :D this is a maps test so this is higher than my level

Citrus2011 [14]

Answer:

Ggghhjjjj

Step-by-step explanation:

5 0

2 years ago

Please help Combine like terms. 9y + 5y - 3 = [? ]y + [ ]