10. (10 points) Determine without solving the problem an interval in which the solution of the...
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
b) (2 points) Determine the largest interval in which the solution of t2y"+3ty +y 0, with y(1) = 0 and y'(1)-1 is certain to exist, without solving this initial value problem
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.
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
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
Find the interval in which the solution of the initial value problem above is certain to exist. |(t - 1)y' (t - 5)y = In|t + t-1, y(10) = -3 (t 5)y'n(t 2)y — 5t, y(3) - 1 |(t - 1)y' (t - 5)y = In|t + t-1, y(10) = -3 (t 5)y'n(t 2)y — 5t, y(3) - 1
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?
Solve the initial value problem and determine the interval in which the solution is valid. Round your answer to three decimal places y′=9x29y2−11, y(1)=0 Solve the initial value problem and determine the interval in which the solution is valid. Round your answer to three decimal places. 31 = avro , Y (1) = 0 3y3 = Qe The solution is valid for Number <<< Number
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