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
valentinak56 [21]
3 years ago
5

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

Mathematics
1 answer:
svetlana [45]3 years ago
6 0

Answer:  The required solution is

y=(-2+t)e^{-5t}.

Step-by-step explanation:   We are given to solve the following differential equation :

y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)

Let us consider that

y=e^{mt} be an auxiliary solution of equation (i).

Then, we have

y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.

Substituting these values in equation (i), we get

m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.

So, the general solution of the given equation is

y(t)=(A+Bt)e^{-5t}.

Differentiating with respect to t, we get

y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.

According to the given conditions, we have

y(0)=-2\\\\\Rightarrow A=-2

and

y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.

Thus, the required solution is

y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.

You might be interested in
Find the sum and express it in simplest form (6u-7c-6)+(-2u+4c)
Daniel [21]
4u+3c-6 is thats what its asking for? just puting the same variables together
4 0
2 years ago
Read 2 more answers
A metric unit of lenght that is equal to one tenth of a meter is
Lelu [443]
It is decimeter :):):)

4 0
3 years ago
What’s the expression of this in simplest form
Ad libitum [116K]

Answer:

3/17

Step-by-step explanation:

3/4 divided by 4  1/4 is = to 3/4 divided by 17/4= 3/4 times 4/17 = 3/17

4 0
2 years ago
Read 2 more answers
The figure shows the design of a greenhouse with a rectangular floor. The front and back sides of the greenhouse are semicircles
Ksju [112]

9514 1404 393

Answer:

  96 cubic feet

Step-by-step explanation:

A volume that is 16 ft by 18 ft by 1/3 ft will be ...

  V = LWH

  V = (16 ft)(18 ft)(1/3 ft) = 96 ft³

96 cubic feet of concrete are needed.

7 0
3 years ago
Maria put trim around a banner that is the shape of a triangle. each side is 22 inches long. maria has 1/2 foot of trim left. wh
marissa [1.9K]
Since Maria is going to put a trim around a triangle-shaped banner with 22 inches long per side, this means that for the banner, it has a total length of 66 inches. 66 inches would be equal to 5.5 foot. This means that the total length of the trim from the start is 7 foot. Hope this helps.
6 0
2 years ago
Other questions:
  • If sin theta = 5/6, what are the values of cos theta and tan theta?
    14·1 answer
  • What is 9/2 in a percentage
    10·2 answers
  • The half-life of uranium-235 is 700 million years. If you start with 50 atoms of it, how many will you have left after 700 milli
    15·2 answers
  • Hannah’s favorite toy character is sold wearing one of many outfits. An outfit consists of one shirt, one pair of pants, and one
    15·1 answer
  • What is the point on a graph at which the graph crosses thd y-axis
    14·2 answers
  • What is the square root
    14·2 answers
  • Dont guess, please..........!
    9·1 answer
  • The marked price of a dozen of copies is Rs 600. If the shopkeeper allows 20% discount and then charges 10% VAT, how many copies
    8·1 answer
  • I need help!il give brainlest
    6·1 answer
  • The z value for a 97. 8% confidence interval estimation is.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!