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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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Step-by-step explanation:

The consecutive integers iincrease by 1. So the middle integer of an odd number of consecutive integers is their mean. Three is an odd number of integers.

45:3 = 15   ← middle number

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Suppose that a child in France pays five euros to visit the zoo. Five euros is the same as $6.80 in the U.S. In France, an adult
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Evaluate the quantity 3 squared times 3 to the power of negative 5 end quantity over 5 to the power of negative two.
chubhunter [2.5K]

The value of the expression given as  [3² * 3⁻⁵]/[5⁻²] is 25/27

<h3>How to evaluate the expression?</h3>

The expression is given as:

3 squared times 3 to the power of negative 5 end quantity over 5 to the power of negative two

Rewrite properly as:

[3² * 3⁻⁵]/[5⁻²]

Apply the negative exponent law of indices

So, we have

[3² * 3⁻⁵]/[5⁻²] = [5²]/[3⁻² * 3⁵]

Apply the exponent law of indices

[3² * 3⁻⁵]/[5⁻²] = [5²]/[3³]

This gives

[3² * 3⁻⁵]/[5⁻²] = 25/27

Hence, the value of the expression given as  [3² * 3⁻⁵]/[5⁻²] is 25/27

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