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
Aleonysh [2.5K]
3 years ago
6

Use differentiation to show that the given function is a solution of the equation for all values of the constants. (Enter your a

nswers in terms of x.) equation: x'' + x = 2et, function x = C1 sin(t) + C2 cos(t) + et
Mathematics
1 answer:
Katena32 [7]3 years ago
8 0

Answer with Step-by-step explanation:

We are given that

DE

x''+x=2e^t

Function:x=C_1sint+C_2cost+e^t

We have to show that given function is  a solution of the equation for all values of the constants.

If given function is  solution of DE then it satisfied the given DE.

Differentiate  function w.r.t.t

x'=C_1cost-C_2sint+e^t

Again differentiate w.r.t. t

x''=-C_1sint-C_2cost+e^t

Substitute the values in the given DE

-C_1sint-C_2cost+e^t+C_1sint+C_2cost+e^t=2e^t

LHS=RHS

Given function satisfied the given DE.Therefore, it is solution of given DE for all values of the constants.

You might be interested in
Which pair of functions are inverse of each other ?
vazorg [7]

Answer:

\sf B. \: f(x) = 5x - 9 \: and \; g(x)=\cfrac{x+9}{5}

Step-by-step explanation:

f(x) = 5x - 9  and g(x) = x+9/5 are inverses of each other.

<u>________________</u>

4 0
1 year ago
Simplify this expression 8+19m-6m
gladu [14]
I am pretty sure that it would be 13m + 8. All you have to do is combine the like terms.
7 0
3 years ago
Does this graph below represent a function? (Yes or no)
Whitepunk [10]

Answer:yes

Step-by-step explanation: it represents a function

4 0
2 years ago
A classroom has 12 students with brown hair, 8 students with black hair, and 5 students with blonde hair. If three students are
aksik [14]
I am going to have to go with, C, because the other answers are Invalid.
4 0
3 years ago
The value of t varies directly with w. When t = 32, the value of w = 56. What is the value of w when t = 92? A 116 B 126 C 161 D
stich3 [128]

Answer:

(D). 182

Step-by-step explanation:

did the math

8 0
2 years ago
Other questions:
  • Principal = ? rate = 3.25 time = 2 years interest = 63.05<br> how is this done?
    7·1 answer
  • Write log4 14 as a logarithm of base 3.
    11·1 answer
  • A book designer decided that the pages of a book should have 1-in. margins at the top and bottom and 1 2 in. margins on the side
    11·1 answer
  • Which value is needed in the expression below to create a perfect square trinomial?
    6·2 answers
  • There is a right isosceles triangle. The hypotenuse is 31. Find the value of the two missing legs. Round the answer to the neare
    9·1 answer
  • 1.338, 1.729, 1.755, 1.153, 1.806, 1.993, 1.45, 1.152, 1.935, 1.095
    15·1 answer
  • Angle= A Round your answer to the nearest hundredth.
    12·1 answer
  • A cash register contains $20 bills and $100 bills with a total value of $1460. if there are 21 bills total, then how many of eac
    10·2 answers
  • Help pweaty pweeeeaaaseee
    5·2 answers
  • Please help i’m stuck in this and don’t know what to do
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!