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
maw [93]
3 years ago
13

Consider the differential equationy′′+3y′−10y=0.(a) Find the general solution to this differential equation.(b) Now solve the in

itial-value problem corresponding to y(0)=2 and y′(0)=10.
Mathematics
1 answer:
RSB [31]3 years ago
6 0

Answer:

Y= 2e^(5t)

Step-by-step explanation:

Taking Laplace of the given differential equation:

s^2+3s-10=0

s^2+5s-2s-10=0

s(s+5)-2(s+5) =0

(s-2) (s+5) =0

s=2, s=-5

Hence, the general solution will be:

Y=Ae^(-2t)+ Be^(5t)………………………………(D)

Put t = 0 in equation (D)

Y (0) =A+B

2 =A+B……………………………………… (i)

Now take derivative of (D) with respect to "t", we get:

Y=-2Ae^(-2t)+5Be^(5t)   ....................... (E)

Put t = 0 in equation (E) we get:

Y’ (0) = -2A+5B

10  = -2A+5B ……………………………………(ii)

2(i) + (ii) =>

2A+2B=4 .....................(iii)

-2A+5B=10 .................(iv)

Solving (iii) and (iv)

7B=14

B=2

Now put B=2 in (i)

A=2-2

A=0

By putting the values of A and B in equation (D)

Y= 2e^(5t)

You might be interested in
Ms. Costo is shopping for a new car. The salesman tells her the price will be $18,795 before a 10% discount. Ms. Costo isn’t sur
Viktor [21]

Answer:

Ms. Costco was offered the best price. It would be $15,900.57 after tax

Step-by-step explanation:

Ms. Costco: $18,795 x .90 =$16,915.50 x .94=$15,900.57

Ms. Deele: $17,050 x .94=$16,027

4 0
2 years ago
A student found the slope of a line that passes through the points (3,15) and (5,9) to be -1/3. what mistake did he make
Vlad [161]

He didn't do it as rise over run, or y2-y1/x2-x1

He did it reverse, which is incorrect.

4 0
3 years ago
The surface area of a square pyramid is found using the formula SA=b^2+2bh, where b is the length of the base and h is the heigh
Genrish500 [490]
The Correct  Answer is C 324
6 0
3 years ago
The convex polygon below has 6 sides. Find the value of x.
MAVERICK [17]

Answer:

it is.............1180 :]

8 0
3 years ago
Which is the graph of the cube root function f(x) = RootIndex 3 StartRoot x EndRoot?
lara [203]

Answer:

<h3>On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).</h3>

Step-by-step explanation:

f(x)=\sqrt[3]{x}\\\\f(-8)=\sqrt[3]{-8}=-2\to(-8,\ -2)\\\\f(0)=\sqrt[3]{0}=0\to(0,\ 0)\\\\f(8)=\sqrt[3]{8}=2\to(8,\ 2)\\\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\text{Therefore:}\\\\\sqrt[3]{-8}=-2\ \text{because}\ (-2)^3=-8\\\sqrt[3]0=0\ \text{because}\ 0^3=0\\\sqrt[3]{8}=2\ \text{because}\ 2^3=8

7 0
3 years ago
Read 2 more answers
Other questions:
  • Use the table to write a linear function that relates y to x.
    6·2 answers
  • Which is the better buy?
    14·2 answers
  • Pls help me with the question above thanks.... AFAP(as fast as possible)
    7·2 answers
  • There are 180 pages in the book Diana is reading. Diana has read 90 pages. What percent of the book has she read?
    15·2 answers
  • The paragraph below comes from the rental agreement Susan signed when she opened her account at Super Video.
    15·2 answers
  • Which is the graph of f(x) = x^2 -2x+ 3
    7·1 answer
  • 5th grade math. correct answer will be marked brainliest
    10·1 answer
  • The president of the student council wants to survey the student population. She decides to take a random sample of
    12·1 answer
  • M measures .<br> ​(a) Find the supplement of M.<br> ​(b) Find the complement of M.
    7·1 answer
  • A)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!