b) (2 points) Determine the largest interval in which the solution of t2y"+3ty +y 0, with...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
10. (10 points) Determine without solving the problem an interval in which the solution of the following initial value problem is certain to exist. (1-9)y'+(In t)y = 421 y(4) = 1
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.
Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist. (Enter your answer using interval notation.) (t - 7)y' + (Int)y = 4, y(1) = 4
Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique solution on (a,b) to the initial value problem below. **x + 3y" - 2xy +y=0y(-)=1.0 (-5) =0.5" (-6) -- o or in interval notation.) (Type your answer in interval notation.)
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
Consider the initial value problem (t-2) y" + cot(t) y' +ty=e', y( 3 ) = 41/3, ' ( 3 ) =- T/ 4. Without solving the equation, what is the largest interval in which a unique solution is guaranteed to exist?
QUESTION 2 Find the longest interval in which the solution for the initial value problem is certain to exist: (t + 2)y" - (sint)y' + - (-1) = 0 a. (- 0,00) O b.(-2,00) oc(- 0,4) d. (-2,0) o e. (-2,4) f. none of the above
(5) Find the solution of the following initial value problems. determine the largest interval in which the solution is va (a) xy + y = ex; y(1) = 1