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
Lady_Fox [76]
3 years ago
15

Verify that y1(t) =t2 and y2(t) =t−1 are two solutions of the differential equation t2y−2y=0 for t > 0.Then show that y=c1t2

+c2t−1 is also a solution of this equation for any c1 and c2.
Mathematics
1 answer:
SIZIF [17.4K]3 years ago
3 0

Answer:

Step-by-step explanation:

Consider first

y_1(t) = t^2\\

We differentiate this two times to get

y_1'(t) = 2t\\y_1"(t) =2

Substitute in the given equation

t^2 (2) -2(t^2 =0

Hence satisfied

Consider II equation

y_2(t) = t^{-1} \\y_2'(t) = - t^{-2}\\y_2"(t) = -2 t^{-3}

Substitute in the given equation to get

t^2 (-2 t^{-3})+2 t^{-1} = 0

Hence satisfied

Together if we have

y = c_1 t^2 +c_2  t^{-1}

being linear combination of two solutions

automatically this also will satisfiy the DE Or

this is a solution to the given DE

You might be interested in
Select the proper order from least to
julsineya [31]

Answer:

4/2, 2/7, 1/2, 5/6 is your answer

8 0
3 years ago
Read 2 more answers
5. Write the conversion factor for converting meters to centimeters.
BARSIC [14]

Answer:

Third option

O 100 cm

1m

Step-by-step explanation:

100cm \div  {10}^{2}  = 1m \\ hope \: this \: helps.. \\ good \: luck

8 0
3 years ago
A recipe calls for 1 ½ cups of flour, 2/3 cup of white sugar, and 1/3 cup of brown sugar. The recipe makes 6 servings. A) How ma
Goryan [66]
<span>A) How many cups of flour are there per serving? 

</span>1 ½ cups of flour --------<span>6 servings
?     cups of flour ------- 1 serving

      </span>1 ½ 
------------ 
        6 

= 3/2 x 1/6
= 1/4

answer: 1/4 cups of flour per serving

<span>B) how many total cups of sugar(white and brown) are there per serving?
</span>total white and brown: <span>2/3 + 1/3 = 3/3 = 1 cups (combine)

1 cup of sugar (white and brown) </span>--------6 servings
? cups of sugar (white and brown) ------ 1 serving

  1
-----  = 1/6
  6
answer: 1/6 cups of sugar (white and brown) per serving

<span> (c) Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe?
</span>
3/2  cups of flour --------6 servings
? cups of flour -----------9 servings


  9 * 3/2             
-----------  
      6

= (13 1/2) / 6
= 2 1/4

2 1/4 ( 9 servings) - 1 1/2(6 servings) = 3/4 cups

answer: you need 3/4 more cups of flour

6 0
3 years ago
Read 2 more answers
Can someone help ?????
Setler [38]

Accordingly the answer is Nineteen Fourths.

8 0
3 years ago
How do I solve proportions? Here’s my questions: <br><br> 1. x/8=5/16<br> 2. 5/12=15/x
Flura [38]

Proportions are very simple once you get the hang of them! What you do is cross multiple. :)

1. x/8=5/16

You first start by multiplying x and 16

Then multiply 5 and 8

So now you have 16x=40

Finally divide 16 from each side

You get: x+0.4!

2. 5/12=15/x

Remember to cross-multiply!

Now we have 5x=180

Next divide 5 from each side

You get: x=36!

7 0
3 years ago
Other questions:
  • Please solve this equation 5-7x=-44​
    15·1 answer
  • Francesca and Will want to find out if the triangle formed by connecting the points G, H, and I is a right triangle.
    10·1 answer
  • What is the simplified form of 9x2-25 divided by 3x+5
    11·1 answer
  • Find the length of the missing side. the triangle not drawn to scale. (Image attached)
    12·2 answers
  • Can some please explain how to do the math
    8·1 answer
  • Find the value of x or y so that the line through the points has the given slope (x, -7) and (3, 3); slope:1
    10·1 answer
  • In a complete paragraph, explain how to scope a speech. <br> Please use your own words.
    13·2 answers
  • Please, someone help? ​
    6·1 answer
  • Need help ASAP!!!!-​
    6·1 answer
  • Need help asap, it's asking me to find m angle J and that K = 25.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!