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Musya8 [376]
3 years ago
6

Solve the differential equation. y' + 5xey = 0.

Mathematics
1 answer:
galben [10]3 years ago
5 0

Answer:

The solution is     y = - ln(\frac{5}{2}x^{2} + C)

Step-by-step explanation:

To solve the differential equation, we will find y

From the given equation, y' + 5xey = 0.

That is, y' + 5xe^{y} = 0

This can be written as

\frac{dy}{dx} + 5xe^{y} = 0

Then,

\frac{dy}{dx} = - 5xe^{y}

\frac{dy}{e^{y}}   = - 5x dx

Then, we integrate both sides

\int {\frac{dy}{e^{y}}}  =\int {- 5x dx}

\int {e^{-y}dy }}  =\int {- 5x dx}

Then,

-e^{-y} = -\frac{5}{2}x^{2} + C

e^{-y} = \frac{5}{2}x^{2} + C

Then,

ln(e^{-y}) = ln(\frac{5}{2}x^{2} + C)

Then,

-y = ln(\frac{5}{2}x^{2} + C)

Hence,

y = - ln(\frac{5}{2}x^{2} + C)

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A= 16 B=28

Step-by-step explanation:

So the ration is 4:7, you have to find multiples that have that same ratio

Multiply both numbers by 4, this should get you

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3 years ago
The weight of mr nazeer is 7 times that of his son. What's the ratio of their weights?
Mekhanik [1.2K]

Answer:

<h3>7:1</h3>

Step-by-step explanation:

Let the weight of mr nazeer be x

Let the weight of his son be y

If the weight of mr nazeer is 7 times that of his son, then x = 7y

To get the ratio of their weight:

Ratio = weight of father/weight of son

Ratio = 7y/y

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3 0
3 years ago
6c-8-2c=-16+c what’s the value of c
Artemon [7]

Answer:

The correct answer is c = -8/3.

Step-by-step explanation:

The first step in solving this problem would be to simplify by combining like terms on the left side of the equation.

6c - 8 - 2c = -16 + c

4c - 8 = -16 + c

Then, we can subtract c from both sides of the equation to get rid of the positive c on the right side of the equation.

4c - c - 8 = -16 + c - c

3c - 8 = -16

Next, we can add 8 to both sides of the equation.

3c - 8 + 8 = -16 + 8

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Then, we can divide both sides of the equation by 3.

c = -8/3

Hope this helps!

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3 years ago
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