Mathematics, 12.10.2020 22:01 Arealbot
Consider the initial value problem
x′ = −tx + x3, x(0) = α,
where α is a parameter.
A) Prove that for α = 1, the solution x(t) grows to infinity (explodes) somewhere on the interval (0,1) completing the following steps
i. Find the solution of initial value problem y′ = y2, y(0) = 1. We denote it y(t) and use in the next steps.
ii. Compute x′(0),x′′(0),x′′′(0),y′(0),y′′(0),y ′′′(0) using differential equations.
iii. Conclude that for small t >0 we have x(t)> y(t) using Taylor formula.
iv. Show thaty(t)>√t on the interval 0< t <1.
v. Show that on the interval 0< t <1 if x(t)> y(t), then (t)((t) - t) > 0)(y(t) - t).
vi. Show that y(t)vº(t) - t) > y(t) on the interval 0
vii. Conclude that if (t) > y(t), then I'(t) > vt).
viii. Conclude that while x(t) is defined, it is greater than y(t). Therefore it explodes to infinity at t = 1 or earlier.
B) Use Matlab to draw a direction field for the differential equation (and attach your graph to your solutions). Observe that there is a critical value of a in the interval 0 Sasi such that if a < 0, then r(t) converges to zero and if a co, then r(t) explodes to infinity.
Answers: 2
Mathematics, 21.06.2019 15:00
The triangles are similar. what is the value of x? show your work.
Answers: 2
Mathematics, 21.06.2019 17:00
The ratio of rock songs to dance songs on jonathan’s mp3 player is 5: 6. the total number of rock and dance songs jonathan has is between 101 120. how many rock songs does he have?
Answers: 2
Mathematics, 21.06.2019 19:30
You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function.how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions
Answers: 2
Mathematics, 21.06.2019 20:30
choose the correct definition for extremo. a. end b. extra c. extract d. eventual
Answers: 2
Consider the initial value problem
x′ = −tx + x3, x(0) = α,
where α is a parameter.
A)...
where α is a parameter.
A)...
History, 26.02.2020 19:49
English, 26.02.2020 19:49
Computers and Technology, 26.02.2020 19:50