In the following problems determine whether existence of at
least one solution of the
given initial value problem is thereby guaranteed and if so,
whether the uniqueness of
that solution is guaranteed. For each initial value problem
determine all solutions and
the intervals where they hold, if the case.
(a) dy/dx = y^(1/3); y(1) = 1.
(b) dy/dx = y^(1/3); y(1) = 0.
(c) dy/dx =sqrt(x - y); y(2) = 1.
Can you explain how can we approach these kind of problems and?
in (iii) initial condition not satisfy..... it is very easy differetial equation.. just seprate both dependent and indendent variable.. and intigrate it...and find solution... any problem i will be always for you. have a good day.
In the following problems determine whether existence of at least one solution of the given initi...
Question 2: A More detailed version of the Theorem 1 at page 24 of the textbook, called Picard's Theorem, says that If the function f(x, y) is continuous in a rectangle near the point (a, b), then at least one solution of the differential equation y' = f(x,y) exists on some open interval I containing the point If, in addition, the partial derivative is also continuous in that rectangle near (a, b), then this solution is unique on some (perhaps...
which one is correct? (12 points) Check the existence and uniqueness of a solution of the following Initial Value Problem: dy = y2 + (x + 2)2 - 1 dx [+(-2) = 1 Yanitiniz: ♡ Existence is guaranteed, uniqueness is guaranteed Existence is guaranteed, uniqueness is not guaranteed Existence is not guaranteed Yaniti temizle Gönder
Determine whether the Existence and Uniqueness of Solution Theorem implies that the given initial value problem has a unique solution. 2 dy Select the correct choice below and fill in the answer box(es) to complete your choice. The theorem implies the existence of a unique solution because a rectangle containing the point Type an ordered pair.) The theorem does not imply the existence of a unique solution becauseis not continuous in any rectangle containing the point Type an ordered pair.)...
Consider the initial value problem x^2 dy/dx = y - xy, y(-1) = 1 Use the Existence and Uniqueness theorem to determine if solutions will exist and be unique. Then solve the initial value problem to obtain an analytic solution.
Determine which of the following initial value problems is correctly associated to the longest interval guaranteed by the existence and uniqueness theorem. y O [0, 4); ty" = 0, y(1) = 0, y (1) = -2 O (5,00); (x – 5)3 dy – 3(x + 2)2 dy CU 3+3 v(2) = -1,v' (2) = 1 1 d.c3 dx2 0(-1,1); 2(t– 1)y" + 3ty - y=et, y(0) = 1, y (0) = 0 (-0,3); xạy" + 2xy – y = 713,...
Solve the given initial value problem and determine at least approximately where the solution is valid. (12x2+y−1)dx−(18y−x)dy=0, y(1)=0 Chapter 2, Section 2.6, Question 10 Solve the given initial value problem and determine at least approximately where the solution is valid. (12x2 + y − 1) dx – (18y – x) d y = 0, y(1) = 0 y = the solution is valid as long as Q@20
In problems 7 and 8 find the solution of the given initial value problem in explicit form: 7. sin 2.x dx + cos 3y dy = 0, y /2) = 1/3. 8. y' (1-22)/2 dy = arcsin x dx, y(0) = 1.
Determine whether a conclusion can be drawn about the existence of uniqueness of a solution of the differential equation 2 drawn, discuss it. If a conclusion cannot be drawn, explain why 4tz' + 2z = cost, given that Z(0) = 2 and 2'(0) - 8. If a conclusion can be Select the correct choice below and fill in any answer boxes to complete your choice. OA. A solution is guaranteed only at the point to = because the functions p(t)...
please show all your work . (6 points) Of the four initial or boundary value problems below, ouly one is guaranteed to have a unique solution according to the Existence and Uniqueness Theorons. Which one i i (a) ty"-Py, + e'y = ), y(1)s 0, V(1) = T. tan (f (b) ty" + 2/-3y = 0, y (0)0. y(0) = 2, y(5) = 0. (d) V, + sec(t)y = sin(2t), . (6 points) Of the four initial or boundary value...
solution for all 4 please In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is. 1. (2xy + cos y) dx + (x2 – x sin y – 2y) dy = 0. 1 dy 2. + cos2 - 2.cy y(y + sin x), y(0) = 1. + y2 dc 3. [2xy cos (2²y) – sin x) dx + x2 cos (x²y) dy = 0. (1+y! x" y® is...