Question

In: Advanced Math

Suppose that m is a fixed positive integer. Show that the initial value problem y' =...

Suppose that m is a fixed positive integer. Show that the initial value problem

y' = y2m/(2m+1) , y(0) = 0

has infinitely many continuously differentiable solutions. Why does this not contradict Picard’s Theorem?

Solutions

Expert Solution


Related Solutions

7. Let m be a fixed positive integer. (a) Prove that no two among the integers...
7. Let m be a fixed positive integer. (a) Prove that no two among the integers 0, 1, 2, . . . , m − 1 are congruent to each other modulo m. (b) Prove that every integer is congruent modulo m to one of 0, 1, 2, . . . , m − 1.
Find the solution of the following initial value problem. y''' + y'' + y' + y...
Find the solution of the following initial value problem. y''' + y'' + y' + y = e^-t + 4cost ; y(0)= 0, y'(0)= -1, y''(0)= 0
1. Consider the initial value problem y′ =1+y/t, y(1)=3 for1≤t≤2. • Show that y(t) = t...
1. Consider the initial value problem y′ =1+y/t, y(1)=3 for1≤t≤2. • Show that y(t) = t ln t + 3t is the solution to the initial value problem. • Write a program that implements Euler’s method and the 4th order Runke-Kutta method for the above initial value problem. Use your program to solve with h = 0.1 for Euler’s and h = 0.2 for R-K. • Include a printout of your code and a printout of the results at each...
Find the solution to the following initial value problem y' -y = t - sint +...
Find the solution to the following initial value problem y' -y = t - sint + e^(2t); y(0) = 0
10. Solve the following initial value problem: y''' − 2y '' + y ' = 2e...
10. Solve the following initial value problem: y''' − 2y '' + y ' = 2e ^x − 4e^ −x y(0) = 3, y' (0) = 1, y''(0) = 6 BOTH LINES ARE PART OF A SYSTEM OF EQUATIONS
Consider the initial value problem y′ = 18x − 3y, y(0) = 2 (a) Solve it...
Consider the initial value problem y′ = 18x − 3y, y(0) = 2 (a) Solve it as a linear 1st order ODE with the method of the integrating factor. (b) Solve it using a substitution method. (c) Solve it using the Laplace transform.
Use the Laplace transform to solve the following initial value problem, y′′ − y′ − 30y  ...
Use the Laplace transform to solve the following initial value problem, y′′ − y′ − 30y  =  δ(t − 7),y(0)  =  0,  y′(0)  =  0. The solution is of the form ?[g(t)] h(t). (a) Enter the function g(t) into the answer box below. (b) Enter the function h(t) into the answer box below.
solve the given initial value problem using the method of Laplace transforms. Y'' + Y =...
solve the given initial value problem using the method of Laplace transforms. Y'' + Y = U(t-4pi) y(0) =1 y'(0) = 0
Use Laplace transforms to solve the initial value problem: x' = 2x + y, y' =...
Use Laplace transforms to solve the initial value problem: x' = 2x + y, y' = 6x + 3y; x(0) = 1, y(0) = -2
Solve the given initial-value problem. y''' − 2y'' + y' = 2 − 24ex + 40e5x,...
Solve the given initial-value problem. y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5 2 , y''(0) = − 5 2
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT