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2 years ago

1) Find the general solution to the following differential equation x^3•y’- y = 0

Mathematics

1 answer:

maxonik [38]2 years ago

6 0

Answer:

y(x) = c_1 e^(-1/(2 x^2))

Step-by-step explanation:

Solve the separable equation x^3 (dy(x))/(dx) - y(x) = 0:

Solve for (dy(x))/(dx):

(dy(x))/(dx) = y(x)/x^3

Divide both sides by y(x):

((dy(x))/(dx))/y(x) = 1/x^3

Integrate both sides with respect to x:

integral((dy(x))/(dx))/y(x) dx = integral1/x^3 dx

Evaluate the integrals:

log(y(x)) = -1/(2 x^2) + c_1, where c_1 is an arbitrary constant.

Solve for y(x):

y(x) = e^(-1/(2 x^2) + c_1)

Simplify the arbitrary constants:

Answer: y(x) = c_1 e^(-1/(2 x^2))

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Please help me with this!!

Naddik [55]

Step-by-step explanation:

To find the y-coordinate points we need to evaluate the function for all the $x$ values in the table. In other words, we need to replace $x$ with each value in our given function and simplify.

- For x = 0

$f(x)=(x-2)^2-5$

$f(0)=(0-2)^2-5$

$f(0)=(-2)^2-5$

$f(0)=4-5$

$f(x)=-1$

Since $x=0$ and $y=-1$ , our first point is (0, -1)

- For x = 1

$f(x)=(x-2)^2-5$

$f(1)=(1-2)^2-5$

$f(1)=(-1)^2-5$

$f(1)=1-5$

$f(x)=-4$

Our second point is (1, -4)

- For x = 2

$f(x)=(x-2)^2-5$

$f(2)=(2-2)^2-5$

$f(2)=(0)^2-5$

$f(x)=-5$

Our third point is (2, -5)

- For x = 3

$f(x)=(x-2)^2-5$

$f(3)=(3-2)^2-5$

$f(3)=(1)^2-5$

$f(3)=1-5$

$f(x)=-4$

Our fourth point is (3, -4)

- For x = 4

$f(x)=(x-2)^2-5$

$f(4)=(4-2)^2-5$

$f(4)=(2)^2-5$

$f(4)=4-5$

$f(x)=-1$

Our fifth point is (4, -1)

Now we just need to plot each point in our coordinate plane and join them with the parabola as you can see in the attached picture.

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2 years ago

Farrah is 4 years older than 5 times her brother Emil's age. Farrah is 19 years old. Let e represent Emil’s age. During the Stra

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The answer is B.
If Farrah is 5 times older than Emil plus 4 years, the equation would be 5e+4.

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2 years ago

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ale4655 [162]

Answer:

Step-by-step explanation:

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2 years ago

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Help me so i can go eat lunch <3 ( question 2)

LekaFEV [45]

<h3>Answer: Choice B</h3>

Doug borrowed $2 from his friend every day from Monday through Friday. How much money does Doug owe in all?

==============================================================

Explanation:

The notation 5(-2) is the same as saying "5 times negative 2"

The negative represents the amount of debt that Doug goes into when borrowing that $2. When borrowing the same amount over the course of 5 days, he'll be in debt a total of 10 dollars. So we'd write -10 to represent this.

You could also write it out the longer way

-2 + (-2) + (-2) + (-2) + (-2) = -10

There are five copies of "-2" being added up to arrive at -10

Though it's much simpler to say

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2 years ago

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alina1380 [7]

<span>y - 4 = 0 so y = 4

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(3, 4) is the solution

answer is </span><span>{(3, 4)} (last choice)</span>

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3 years ago

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