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
melomori [17]
3 years ago
8

Solve y' + 2xy = 2x^3, y(0) = 1

Mathematics
1 answer:
nlexa [21]3 years ago
6 0
Multiply both sides by e^{x^2}, then you get

e^{x^2}+2xe^{x^2}y=2x^3e^{x^2}
\left(e^{x^2}y\right)'=2x^3e^{x^2}
e^{x^2}y=\displaystyle2\int x^3e^{x^2}\,\mathrm dx
e^{x^2}y=e^{x^2}(x^2-1)+C
y=x^2-1+Ce^{-x^2}

Given that y(0)=1, you have

1=-1+Ce^0\implies C=2

so that the particular solution is

y=x^2-1+2e^{-x^2}
You might be interested in
4w + x + 2y - 3z= -16
barxatty [35]
See photo. I hope it helps

3 0
3 years ago
Write a linear function f with f(0)=7 and f(3)=1.
choli [55]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

a = ( 0 , 7 ) & b = ( 3 , 1 )

First need to find the slope using the following equation :

slope =  \frac{y(b) - y(a)}{x(b) - x(a)}  \\

slope =  \frac{1 - 7}{3 - 0}  \\

slope =  \frac{ - 6}{3}  \\

slope =  - 2

_________________________________

We have following equation to find the point-slope form of the linear functions using the slope and one of the through points .

y - y(0) = m \times ( \: x - x(0) \: )

x(0) = x - coordinate \:  \: of  \:  \: through \:  \: point \\

y(0) = y - coordinate \:  \: of \:  \: through \:  \: point \\

m = slope

I choose point (( a )) to put in the equation.

y - 7 =  - 2 \times (x - 0)

y - 7 =  - 2x  + 0

y - 7 =  - 2x

Add sides 7

y - 7 + 7 =  - 2x + 7

y =  - 2x + 7

This the slope-intercept form .

Done...

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

7 0
2 years ago
In slope-intercept form, what is the equation of the line passing through the points
Murljashka [212]

Answer:

03) y≈-3x±11

Step-by-step explanation:

6 0
2 years ago
Which is an equation in point-slope form for the given point and slope?
Mashutka [201]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 4 and (a, b) = (- 3, 7), hence

y - 7 = 4(x - (- 3)), that is

y - 7 = 4(x + 3) ← second equation in the list

7 0
3 years ago
Equation A: y = 2x + 4
Ymorist [56]
2x+4=3x+1 they've substituted y =2x+4 into the second eq.
6 0
3 years ago
Other questions:
  • As saturn revolves around the sun, it travels at a speed of approximately 6miles per second. convert this speed to miles per min
    10·1 answer
  • in a parallelogram with area of 40, a side is 3 less than the altitude drawn to that side. Find the altitude of the parallelogra
    9·1 answer
  • How would u solve this
    9·1 answer
  • Solve (3x−2)(x+12)=0, for x.
    15·1 answer
  • Somebody please explain this to me and help me!!!
    13·2 answers
  • Help whats the value of x
    8·2 answers
  • I'll mark you as the brainiest if you get this correct thx xxx This homework is due tomorrow thx for your help
    14·2 answers
  • 27 minus ³/² of a number(x) is not more than 36. What is the number
    15·1 answer
  • How manyy solutions does this system of equations have? explain how you know y + 2x = 5 y = 3x + 5
    6·1 answer
  • Expand.<br> Your answer should be a polynomial in standard form.<br> (x-3)(x-4)=
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!