In Exercises 1-13 find all (xo, Vo) for which Theorem 2.3.1 implies that the initial value problem f(z. y), y(zo)-Yo has (a) a solution (b) a unique solution on some open interval that contains 10
3. tanry
y'=ln(1+12 +ข้า 7.
Homework Answers
Add Answer to:
Theorem 2.3.1 If f is continuous on an open rectangle (a) that contains (xo yo) then the initial value problem f(a, y), y(o)yo has at least one solution on some open subinterval of (a, b) that co...
If f(x, y) is continuous in an open rectangle R = (a, b) x (c, d)...
If f(x, y) is continuous in an open rectangle R = (a, b) x (c, d) in the xy-plane that contains the point (xo, Yo), then there exists a solution y(x) to the initial-value problem dy = f(x, y), y(xo) = yo, dx that is defined in an open interval I = (a, b) containing xo. In addition, if the partial derivative Ofjay is continuous in R, then the solution y(x) of the given equation is unique. For the initial-value...
For each initial value problem, does Picards's theorem apply? If so, determine if it guarantees that...
For each initial value problem, does Picards's theorem apply? If
so, determine if it guarantees that a solutio exists and is
unique.
Theorem (Picard). Consider the initial value problem dy = f(t,y), dt (IVP) y(to) = Yo- (a) Existence: If f(t,y) is continuous in an open rectangle R = {(t,y) |a<t < b, c < y < d} and (to, Yo) belongs in R, then there exist h > 0 and a solution y = y(t) of (IVP) defined in...
2y (9 points) Given the initial value problem y' => y (xo) = yo. Use the...
2y (9 points) Given the initial value problem y' => y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where xo + 0, b) no solution exists if y (0) = yo # 0, and c) an infinite number of solutions exist if y (0) = 0.
x (9 points) Given the initial value problem y' 2y 29, 2014 ,y (xo) = yo....
x (9 points) Given the initial value problem y' 2y 29, 2014 ,y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where Xo 70, b) no solution exists if y (0) = yo #0, and c) an infinite number of solutions exist if y (0) = 0.
Theorem 2.1 Consider an IVP of the form y' + g (x)ya h(x), y(%)-yo. Assume that g(x) and h(x) are both continuo...
Theorem 2.1 Consider an IVP of the form y' + g (x)ya h(x), y(%)-yo. Assume that g(x) and h(x) are both continuous on some interval a < x < b and that a < xo < b. Then there exists a unique solution y(x) to the initial value problem that is defined on a <x<b Theorem 2.2 Consider an IVP of the form y' = f (x.y), y(xo) = yo. Assume that ftxy) andfx, y) are both continuous on a...
1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has a unique and continuous solution φ(t) on a s...
1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has a unique and continuous solution φ(t) on a small interval containing to, φ(t) satisfies the initial condition φ(to) = to.
1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has...
2y 1. (9 points) Given the initial value problem y' = y (xo) = yo. Use...
2y 1. (9 points) Given the initial value problem y' = y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where x, 60, b) no solution exists if y(0) = % 70, and c) an infinite number of solutions exist if y(0) = 0.
29. (a) Without solving, explain why the initial-value problem dy dx vy, y(xo) = yo has...
29. (a) Without solving, explain why the initial-value problem dy dx vy, y(xo) = yo has no solution for yo < 0. (b) Solve the initial-value problem in part (a) for yo > 0 and find the largest interval / on which the solution is defined
Question 2: A More detailed version of the Theorem 1 at page 24 of the textbook, called Picard's ...
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...
Prove that the following two-point boundary-value problem has a UNIQUE solution. Thank you Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and...
Prove that the following two-point boundary-value problem has a
UNIQUE solution.
Thank you
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
If f(x, y) is continuous in an open rectangle R = (a, b) x (c, d) in the xy-plane that contains the point (xo, Yo), then there exists a solution y(x) to the initial-value problem dy = f(x, y), y(xo) = yo, dx that is defined in an open interval I = (a, b) containing xo. In addition, if the partial derivative Ofjay is continuous in R, then the solution y(x) of the given equation is unique. For the initial-value...
For each initial value problem, does Picards's theorem apply? If
so, determine if it guarantees that a solutio exists and is
unique.
Theorem (Picard). Consider the initial value problem dy = f(t,y), dt (IVP) y(to) = Yo- (a) Existence: If f(t,y) is continuous in an open rectangle R = {(t,y) |a<t < b, c < y < d} and (to, Yo) belongs in R, then there exist h > 0 and a solution y = y(t) of (IVP) defined in...
2y (9 points) Given the initial value problem y' => y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where xo + 0, b) no solution exists if y (0) = yo # 0, and c) an infinite number of solutions exist if y (0) = 0.
x (9 points) Given the initial value problem y' 2y 29, 2014 ,y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where Xo 70, b) no solution exists if y (0) = yo #0, and c) an infinite number of solutions exist if y (0) = 0.
Theorem 2.1 Consider an IVP of the form y' + g (x)ya h(x), y(%)-yo. Assume that g(x) and h(x) are both continuous on some interval a < x < b and that a < xo < b. Then there exists a unique solution y(x) to the initial value problem that is defined on a <x<b Theorem 2.2 Consider an IVP of the form y' = f (x.y), y(xo) = yo. Assume that ftxy) andfx, y) are both continuous on a...
1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has a unique and continuous solution φ(t) on a small interval containing to, φ(t) satisfies the initial condition φ(to) = to.
1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has...
2y 1. (9 points) Given the initial value problem y' = y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where x, 60, b) no solution exists if y(0) = % 70, and c) an infinite number of solutions exist if y(0) = 0.
29. (a) Without solving, explain why the initial-value problem dy dx vy, y(xo) = yo has no solution for yo < 0. (b) Solve the initial-value problem in part (a) for yo > 0 and find the largest interval / on which the solution is defined
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...
Prove that the following two-point boundary-value problem has a
UNIQUE solution.
Thank you
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
Most questions answered within 3 hours.
-
Twitter Users and News: A poll conducted in 2013 found that 52%
of U.S. adult Twitter...
asked 4 minutes ago -
How
would I know whether a given amino acid has an ionizable group or
not? please...
asked 12 minutes ago -
True or false?
True False The function of the enzyme acyl CoA
synthetase is the ATP-dependent coupling...
asked 12 minutes ago -
Nadia Corporation adjusts its debt so that its interest coverage
(EBIT/Interest) remains constant at 3. Nadia’s...
asked 14 minutes ago -
In a clinical trial, 20 out of 600 patients taking a
prescription drug complained of flulike...
asked 20 minutes ago -
7. How many types of nuclear processes can produce energy? 8.
How many types of radioactive...
asked 24 minutes ago -
For both the Sn2 and Sn1 reaction
conditions:
Structure | Rxn (Y/N) at room T° Rxn...
asked 24 minutes ago -
11. In cell N2, enter a formula using the IF function and a
structured reference to...
asked 24 minutes ago -
There is X-linked mutations in flies in this example. You need
to determine the inheritence pattern...
asked 26 minutes ago -
1) There is a 5.0 μC charge at each of 3 corners of a square
(each...
asked 37 minutes ago -
A study of 420,095 cell phone users found that
134 of them developed cancer of the...
asked 41 minutes ago -
2.50 g of NH4Cl is added to 12.9 g of water. Calculate the
molality of the...
asked 43 minutes ago