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
vladimir2022 [97]
3 years ago
9

D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
8 0
The solution depends on the value of k. To make things simple, assume k>0. The homogeneous part of the equation is

\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0

and has characteristic equation

r^2-16k=0\implies r=\pm4\sqrt k

which admits the characteristic solution y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}.

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be y_p=ae^{4x}+be^x. Then

\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x

So you have

16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x
(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x

This means

16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}
b(1-16k)=30\implies b=\dfrac{30}{1-16k}

and so the general solution would be

y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x
You might be interested in
The town of Passaic had 58,753 people in 1990 and 71,509 people in 2014.
OLEGan [10]

Answer:

21.71% increase

Step-by-step explanation:

increase = Increase ÷ Original Number × 100

12756/58753*100

0.217112318*100

21.71% increase.

MARK ME BRAINLIEST

7 0
2 years ago
13. Is the following the graph of a function? Why or why not? ​
Semenov [28]
No. To test whether a graph is a function or not you do the vertical line test where if a vertical line touches more than one point it is not a function
7 0
3 years ago
1. Find an algebraic representation for an exponential function if it is known that f(x + 1) = 4.f(x)
MrMuchimi

f(x)=4^{x-1} is the algebraic representation for an exponential function

Step-by-step explanation:

Given:

f(x + 1) = 4.f(x)

f(3) = 16

To Find:

Algebraic representation for an exponential function=?

Solution:

From the formula f(x+n) = 4^n f(x)

when n= 1, x= 3

f(3+1)= 4(1)f(3)

f(4)= 4f(3)

Substituting the value of f(3)

f(4)= 4f(3)

f(4)= 4 x 16  

f(4)= 64

f(4)=4^2

f (5) = 4^2 x 16

f (5) = 4^2 x  4^2

f(5)= 4^4

Similarly,

F(6) = 4^5

Hence, f(x)=4^{x-1}

4 0
3 years ago
Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature e
Naily [24]
I don’t have the time for my birthday but I’m just asking for a little
7 0
3 years ago
Maya is learning to drive, so this weekend she practiced driving 1/2 of a mile with her mother and another 3/4 of a mile with he
vitfil [10]

Step-by-step explanation:

1/2 + 3/4

= 2/4 + 3/4

= 5/4

= 1 and 1/4 miles

6 0
3 years ago
Other questions:
  • Pleaseeeeeee help meeee!!!!!!!!!!!!
    11·1 answer
  • The hypotenuse of a right triangle is 7 inches, and one of the legs is inches. Find the length of the other leg. .
    13·1 answer
  • Please Help !!! Thank You
    15·2 answers
  • Use truth tables to show that the following statements are logically equivalent. ∼ P ⇔ Q = (P ⇒∼ Q)∧(∼ Q ⇒ P)
    12·1 answer
  • Can someone help I’m not sure if I got this problem right
    6·1 answer
  • Lamar earns 40% of her daily earnings moving furniture if she earns $150 in total on one day how much money did she earn moving
    7·1 answer
  • The graphs of linear functions f and g are shown on the grid.
    8·2 answers
  • I need help with this
    7·1 answer
  • Please help me with this problem
    7·2 answers
  • If a parallelogram has congruent
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!