(5) Find the solution of the following initial value problems. determine the largest interval in which...
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
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.)
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’...
solve 5c 5. (24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y (1) = 0 (Bernoulli equation) 18 b) y" – 4y' – 12y = 3e5, y (0) =- (Hint: use the method of undetermined 7 coefficients) c) (2xy - 9x?) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE)
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
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
(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
Determine which of the following initial value problems is correctly associated to the longest interval guaranteed by the existence and uniqueness theorem. y O [0, 4); ty" = 0, y(1) = 0, y (1) = -2 O (5,00); (x – 5)3 dy – 3(x + 2)2 dy CU 3+3 v(2) = -1,v' (2) = 1 1 d.c3 dx2 0(-1,1); 2(t– 1)y" + 3ty - y=et, y(0) = 1, y (0) = 0 (-0,3); xạy" + 2xy – y = 713,...
(24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y(1) = 0 (Bernoulli equation) 18 1 b) y" – 4y - 12y = 3e St, y (0) = , y'(0) - (Hint: use the method of undetermined coefficients) c) (2xy - 9x) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE) = -1 7
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