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oksian1 [2.3K]
4 years ago
15

Find the solution of the differential equation that satisfies the given initial condition.

Mathematics
1 answer:
andriy [413]4 years ago
5 0
\displaystyle \frac{dy}{dx} = \frac{x}{y} \ \Rightarrow\ y \,dy = x\, dx\ \Rightarrow\textstyle \ \int y \,dy = \int x\, dx\ \Rightarrow\  \frac{1}{2}y^2 = \frac{1}{2}x^2 + C \Rightarrow \\ \\
y(0) = -3\ \Rightarrow\ \frac{1}{2}(-3)^2 = \frac{1}{2}(0)^2 + C\ \Rightarrow\ C = \frac{9}{2},\\ \\
 \text{so } \frac{1}{2}y^2 = \frac{1}{2}x^2 + \frac{9}{2}\ \Rightarrow\ y^2 = x^2 + 9 \ \Rightarrow \ \\ \\
y = -\sqrt{x^2 + 9}\ \text{  since $y(0) = -3 \ \textless \  0$}
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Help brainliest
iris [78.8K]

Answer:

y = - \frac{4}{3} x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (- 3, 3) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = \frac{-1-3}{0+3} = - \frac{4}{3}

The line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - \frac{4}{3} x - 1 ← equation of line

4 0
3 years ago
Evaluate (6x+3y)-z^(2)÷(2x) when x=-3,y=4,z=-6
irina1246 [14]
<h2>Answer:</h2>

<u>24.</u>

<h2>Step-by-step explanation:</h2>

<h3>1. Write the expression.</h3>

(6x+3y)-\frac{z^{2}}{(2x)}

<h3>2. Substitute the variables by the respective given value using <u>parenthesis</u>.</h3>

(6(3)+3(4))-\frac{(6)^{2}}{(2(3))}

<h3>3. Simplify the expression by applying the hierarchy or mathematical operations.</h3>

<em>a) Solve parenthesis.</em>

(18+12)-\frac{(6)^{2}}{6}\\ \\30-\frac{(6)^{2}}{6}

<em>b) Solve the exponent.</em>

30-\frac{36}{6}

<em>c) Divide.</em>

30-6

<em>d) Subtract.</em>

24.

7 0
2 years ago
Find the constant of variation k for the inverse variatio. Then write an equation for the inverse variation y=5 x=7.5
lisabon 2012 [21]

Answer:

K= 0.6 with the repeating 6.

the equation is     y= 0.6x    with the repeating 6

hope this helps!


Step-by-step explanation:


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3 years ago
Use chords to solve fox.
dimaraw [331]

Answer:

x=70

Step-by-step explanation:

it is because equal chord cuts off equal arc.....

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4 years ago
In the equation y = 6.7x, what is the constant of proportionality
devlian [24]

The constant in an equation would be the number multiplied to x,

In the equation y - 6.7x, the constant would be 6.7

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3 years ago
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