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
makvit [3.9K]
3 years ago
8

Verify by substitution that the given function is a solution of the given differential equation.x2y′′ + xy′ −y = ln x, y = x −ln

x
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
4 0

Looks like the differential equation is

x² y'' + x y' - y = ln(x)

and the known solution is

y = x - ln(x)

Take the first derivatives of the solution:

y' = 1 - 1/x

y'' = 1/x²

Substitute y and its derivatives into the DE:

x² (1/x²) + x (1 - 1/x) - (x - ln(x)) = ln(x)

If y is a valid solution, then this equation should reduce to an identity.

1 + x - 1 - x + ln(x) = ln(x)

0 = 0   ✓

You might be interested in
Mary Jo spends $1,450 to buy stock in two companies. She pays $15 a share to one of the companies and $20 a
GREYUIT [131]

Answer:

she bought 70 shares of the $15 shares

she bought 20 shares of the $20 shares

Step-by-step explanation:

this would be solved using simultaneous equation

let a = $15 shares

b = 20 shares

a + b = 90   equation 1

15a + 20b = 1450  equation 2

Multiply  equation 1  by 15

15a + 15b = 1350  equation 3

subtract  equation 3 from  equation 2

5b = 100

b = 20

substitute for b in  equation 1

20 + a = 90

a = 70

3 0
3 years ago
A shade of orange paint is made with 5 parts red paint and 15 parts yellow paint. what percent of the paint is red? what is the
Volgvan
1/4           . . . . ........ .. . . .  . . . . .. . .. . . .. . . . 
                                                               
3 0
4 years ago
Pls help I’ll brainlest ASAP I’ll add extra points
FromTheMoon [43]

Answer:

I think the slope is -1/-4 or - 1/4

3 0
2 years ago
Solve for a<br><br>[<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%2B2%7D%7B3%7D%20%3D%20%5Cfrac%7Ba-4%7D%7B6%7D%20" id="TexFo
Lady bird [3.3K]

\frac{a + 2}{3}  =  \frac{a - 4}{6}  \\ 6(a + 2) = 3(a - 4) \\ 6a + 12 = 3a - 12 \\ 3a =  - 24 \\ a =  - 8
5 0
3 years ago
Please help with this question !! Molly earned $430 mowing lawns over the summer. She put 60% of what she earned into her saving
Mrac [35]

Answer:

  $258

Step-by-step explanation:

60% of $430 is ...

  0.60 × $430 = $258

Molly put $258 into her savings account.

3 0
3 years ago
Read 2 more answers
Other questions:
  • Trish is taking care of the Han family's dogs. The Hans leave 7 cans of dog food for the 3 days they'll be away. How much food w
    9·2 answers
  • X^2-24x+9=0<br><br> Show your work.<br><br> Plz help!
    11·1 answer
  • HELP ASAP I WILL GIVE BRAINLIEST
    15·1 answer
  • What is the best measure of center? <br> a. range<br> b.median<br> c.mean<br> d.mode
    9·1 answer
  • PLEASE HELP ME ANSWER THESE QUESTIONS
    14·1 answer
  • HELP<br> find the solution set of the inequality 15x-4 &lt; 29.
    11·1 answer
  • What is the estimate of the product 11/12 x 4/5​
    15·1 answer
  • Pls help help help help help ​
    14·1 answer
  • How do i make f(x)=3(4)^x​
    7·1 answer
  • Hi guys I need help<br><br><br><br><br><br>please<br><br><br><br><br><br><br>​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!