1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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)

You might be interested in
Answer this and i will never forget about you. ever.
trasher [3.6K]

Answer:

I believe that A is the correct answer.

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
What is the area of a circle that has a diameter if 6 inches?
Taya2010 [7]

Answer:

28.27

Step-by-step explanation:

A=(1/4) πd^2

6 0
3 years ago
Read 2 more answers
Three students were given the expression shown to simplify<br><br> 1-8(10x-3)​
madreJ [45]

Answer:

-70x + 21

Step-by-step explanation:

1-8(10x-3)

-7(10x-3)

Use distributive property

-70x + 21

(This is how we learned to do it in my school)

6 0
3 years ago
Read 2 more answers
Christy purchased an art easel at a garage sale for $30. She later sold the easel on Craigslist for $45. What was the percent in
Zielflug [23.3K]

The percent increase by 15%

4 0
2 years ago
Read 2 more answers
Sin (x/2)= √2- sin (x/2) solve for the exact solutions in the interval (0, 2π)
serg [7]

sin\left( \frac{x}{2} \right)=\sqrt{2}-sin\left( \frac{x}{2} \right)\implies sin\left( \frac{x}{2} \right)+sin\left( \frac{x}{2} \right)=\sqrt{2}\implies 2sin\left( \frac{x}{2} \right)=\sqrt{2} \\\\\\ sin\left( \cfrac{x}{2} \right)=\cfrac{\sqrt{2}}{2}\implies sin^{-1}\left[ sin\left( \cfrac{x}{2} \right) \right]=sin^{-1}\left( \cfrac{\sqrt{2}}{2} \right) \implies \cfrac{x}{2}= \begin{cases} \frac{\pi }{4}\\\\ \frac{3\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill

\cfrac{x}{2}=\cfrac{\pi }{4}\implies \boxed{x=\cfrac{\pi }{2}}~\hfill \cfrac{x}{2}=\cfrac{3\pi }{4}\implies \boxed{x=\cfrac{3\pi }{2}}

5 0
3 years ago
Other questions:
  • [100 POINTS]!!!!!!!!!<br> Please Help! Serious answers please
    9·2 answers
  • Mean mode median range
    5·1 answer
  • If 3t - 7 = 5t, then 6t = <br> A. 21 <br> B. -7 <br> C. -21<br> D. -42
    13·1 answer
  • 3/4 x 5/6 equals what
    15·1 answer
  • Please help me!!<br> F)...<br> G)....<br> H)....<br> J)....
    14·1 answer
  • II. The Añejo Rum 45 played 5 games. Find the total of poin
    10·1 answer
  • Craig likes to collect records. Last year he had 10 records in his collection. Now he has 11 records. What is the percent increa
    12·1 answer
  • Sally rolled a 6-sided number cube 40 times and it landed on 4 eight times. What is the experimental probability of Sally gettin
    12·1 answer
  • The measure of 2WXZ is 100°.<br> What is the measure of ZYXZ?
    9·1 answer
  • The Garden Task
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!