1. Show that the following initial value problem has a unique solution and find the solution....
1. (5 points) Find an interval containing x 0for which the given initial value problem has a unique solution. y=x2 +2 +cos(x 1. (5 points) Find an interval containing x 0for which the given initial value problem has a unique solution. y=x2 +2 +cos(x
Find the solution ?y of the initial value problem ?″(?)=49(?′(?))10?5,?(1)=0,?′(1)=1. ?(?)= (10 points) Find the solution y of the initial value problem 4 (v(1) 10 y (t) = y(1) = 0, y (1) = 1. y(t) = (1/^4)^(1/9) Σ Help Entering Answers Preview My Answers Submit Answers Show me another Results for this submission Entered Answer Preview Result [1/(t^4)]^(1/9) C) incorrect
do 2 and 3 Example 2.4. Find a solution to the initial value problem tion of variables. = xy'), y(0) = 0 by separa- = 220/2 dx dy =xda yv f yolkdy - freda 1/2 y 2 Vy = 22 + c y colo 200) = 0 + c cao = 25 = 22 - ² - 4 Vy Show that the theorem on eristence and uniqueness of first-order initial value problems (See See ) does not guarantee that this...
Exercise 1 Consider the initial-value problem y(t)=1+3940), 25t<3; y(2) = 0. a) Show that the problem has a unique solution. b) Compute (by hand) an approximation of y(3) using the forward Euler method with a step size h = 0.5 (namely perform 2 steps of the method).
please show all steps (a) Find the Laplace transform of the solution of the initial-value problem y" - 4y + 3y = -3x + 2 cos(3x), y(0) = 2, y (0) = 3. 8² +68 is the Laplace transform of the solution of an intitial-value problem. Find the (8 + 1)(82 +9) solution y = y(a) by finding the inverse transform of Y.
6. (2 pts) Consider the following initial value problem: y' = (t + y)?y2 + sin(yº) + yety, y(0) = 0. This initial value problem satisfies the existence and uniqueness theorem criteria using interval (-0, 0) for both thet and y variables, and hence has a unique solutoin. Find this unique solution. Hint: None of the techniques we've learned for explicitly solving will work. Instead, try plugging the initial condition into the differential equation and think about what that tells...
The objective of this question is to find the solution of the following initial-value problem using the Laplace transform. The objective of this question is to find the solution of the following initial-value problem using the Laplace transform y"ye2 y(0) 0 y'(0)=0 [You need to use the Laplace and the inverse Laplace transform to solve this problem. No credit will be granted for using any other technique]. Part a) (10 points) Let Y(s) = L{y(t)}, find an expression for Y(s)...
(1 point) Find the solution to initial value problem ,dy – 14 + 49y = 0, y(0) = 2, y(0) = 3 dt g(t) =
Problem 1. Find the solution to the following initial value problems. (a) y'" – y" – 4y' + 4y = 0; y(0) = -4, y'(0) = -1, y"(0) = -19. (b) y'' – 4y"' + 7y – by = 0; y(0) = 1, y'(0) = 0, y"(O) = 0.
(A) Find the largest x-interval where the initial value problem has a unique solution: Where A, B, C, D, E, F are some known constants. (B) Determine whether the set of functions could form a fundamental set of solution of a linear differential equation Thank you We were unable to transcribe this image5, sinx, cos2.c