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Annette [7]
2 years ago
8

Giải phương trình vi phân a. dy/dx b. y' + 2xy = 4x

Mathematics
1 answer:
WITCHER [35]2 years ago
8 0

Your first differential equation is incomplete, so I'll just look at the second one.

<em>y'</em> + 2<em>xy</em> = 4<em>x</em>

Multiply both sides by exp(<em>x</em> ²):

exp(<em>x</em> ²) <em>y'</em> + 2<em>x</em> exp(<em>x</em> ²) <em>y</em> = 4<em>x</em> exp(<em>x</em> ²)

The left side is the derivative of a product:

(exp(<em>x</em> ²) <em>y</em> )<em>'</em> = 4<em>x</em> exp(<em>x</em> ²)

Integrate both sides:

exp(<em>x</em> ²) <em>y</em> = ∫ 4<em>x</em> exp(<em>x</em> ²) d<em>x</em>

For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em> :

exp(<em>x</em> ²) <em>y</em> = 2 ∫ exp(<em>u</em>) d<em>u</em>

Solve for <em>y</em> :

exp(<em>x</em> ²) <em>y</em> = 2 exp(<em>u</em>) + <em>C</em>

exp(<em>x</em> ²) <em>y</em> = 2 exp(<em>x</em> ²) + <em>C</em>

<em>y</em> = 2 + <em>C</em> exp(-<em>x</em> ²)

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2 years ago
Two-thirds of a class are boys. If there are 12 boys, then<br> how many girls are in the class?
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Step-by-step explanation:

so 2/3 OF the class are boys...

***REMEMBER IN MATHEMATICS, ^OF^ IS USED TO SAY MULTPLICATION***

so 2/3 OF class(x) are boys and there are 12 boys...

so 2/3 * x = 12

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to solve use the Keep, Change, Flip method

Keep 12, change / to multiplication, flip 2/3 to 3/2

it becomes 12 * 3/2 and to solve easier 12 is same thing as 12/1

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So the class has 18 students, and 2/3 of boys (12 of the students)

we can solve for how many girls are in the class

Depending on how your teacher wants to see the work:

either 18 - 12 = 6

or 1/3 * 18 which we rewrite as 1/3 * 18/1 = (1*18)/(3*1) which is 18/3... simplified it is  6

There are 6 girls in the class.

Hope this helps! :)

6 0
2 years ago
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Step-by-step explanation:

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