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 init...
1. (a) Determine the largest x-interval where the initial value problem has a unique solution: 1 1 (22 – 40) (6) + y(5) + (x + 1)y" + e*y' + (tan x)y In (x – 1) x2 9 = = = with y(2.5) A, Y' (2.5) B, y" (2.5) C, y'" (2.5) D, y(4) (2.5) y(5)(2.5) = F, where A, B, C, D, E, and F are some known constants. E, (b) Determine whether the set of functions {5, sin’...
Question 1: (20 points) Find the solution of the initial value problem a = cos? x – sin x – 2y cos x + y2 , y(0) = given that yi(2) = cos x is a solution of the differential equation.
5. Find the largest interval a <t<b such that a unique solution of the given initial value problem is guaranteed to exist. (t +3)x' = 4x + 5y x(1) = 0 (t - 3)x' = 3x + 4ty y(1) = 2 Show work
3. (20 points) Find the solution y = y(x) of the initial value problem y 0 − y x = cos2 (y/x) , y(1) = π 3 3. (20 points) Find the solution y = y(x) of the initial value problem 37 - = cos”(y/2),y(1) = 5
Problem 4 ( 14 points) (a) Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution. (t +3)(t - 5)/" + 3ty' + 4y = 2, y(3) = 0, y(3) = -1. (b) Find the Wrongskian of two solutions of the following equation without solving the equation. (t2 – 1)y" – (t – 1)(t + 1)(t + 2)y' + (t + 2)y = 0.
Problem 4 ( 14 points) (a) Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution. (t +3)(t - 5)/" + 3ty' + 4y = 2, y(3) = 0, y(3) = -1. (b) Find the Wrongskian of two solutions of the following equation without solving the equation. (t2 – 1)y" – (t – 1)(t + 1)(t + 2)y' + (t + 2)y = 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
4. (10 points)Determine the longest interval in which the given initial value problem is certain to have a unique solution. Explain. t(t? - 1)/" - 2 tan(t)y - 3y = 12 y(4) = 2,v/(4) = -2
4. Find the longest r-interval where the initial value problem: y'+ty: = tany, y(-1) = 1 has a unique solution. (10 points)
Find the solution to the initial value problem: dy dy/dx=x^ 2√1 + x^3/1+cos y y(0)=2 the 1+x^3 is all in square root.