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Please show all work! (a) Determine the largest r-interval where the initial value problem has a...
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’...
(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
HELLO I AM CURRENTLY IN DIFFERENTIAL EQUATIONS PLEASE EXPLAIN EACH STEP SO I CAN LEARN FROM YOU (I KNOW SOME PEOPLE ONLY CARE ABOUT TEH ANSWER, BUT WILL REALLY APPRECIATE IT) TO SAVE TIME FEEL FREE TO JUST SAY A LAW, THEOREM, OR CONCEPT FOR AN EXPLANATION AND I CAN GO AHEAD AND STUDY IT ON MY OWN. i REALLY DO READ THESE VERY CAREFULLY AND USE THE COMMENTS OFTEN, SO JUST A LITTLE HEADS UP. I FIND IT DIFFICULT...
Previous Problem Problem List Next Problem (1 point) Note WeBWork will interpret acos(z) as cos (z), so in order to write a times cos(z) you need to type a cos(z) or put a space between them. The general solution of the homogeneous differential equation can be written as e-acos(x)+bsin(z) where a, b are arbitrary constants and 1r is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation y" + ly-2ez is บ-Uc + so...
Please show all your work HW3: Problem 7 Previous Problem Problem List Next Problem (1 point) Fundamental Existence Theorem for Linear Differential Equations Given the IVP dz1 d"y d" - 4.(2) +4-1(2) +...+41 () dy +40()y=g(2) dr y(t) = yo, y(t)= y yn-1 (3.) = Yn1 If the coefficients (1),..., Go() and the right hand side of the equation g(1) are continuous on an interval I and if (1) #0 on I then the IVP has a unique solution for...
(1 point) The general solution of the homogeneous differential equation can be written as 2 where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation 2y 5ryy 18z+1 isyp so yax-1+bx-5+1+3x NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) 3, y'(1) 8 The fundamental theorem for linear IVPs shows that this solution is the unique solution to...
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 solution of the following initial value problems. determine the largest interval in which the solution is va (a) xy + y = ex; y(1) = 1
Please show all work with clear handwriting a) Compute the Wrornskian of the set {e* cos 3x, ex sin 3x} b. Show that {ex cos 3x, ex sin 3x} form a fundamental solution set for y" – 2y' +10y = 0 on the interval (-00,00) and write the general solution
#1 part a and b please write solutions neatly 1. (16 points) Determine whether the given set of functions is linearly dependent or linearly independent on the indicated interval. Justify your answers. (a) (8 points) f(x) = x + 2 cos?x, f?(x) = 3sin?x, f(x) = x+2 on (-0,0). (b) (8 points) f (x) = ed" and 12(x) = e 4s are solutions of the linear homogeneous differential equation y" + y' - 12y = 0 on (-0,0).