(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
(A) Find the largest x-interval where the initial value problem has a unique solution: Where 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’...
Please show all work! (a) Determine the largest r-interval where the initial value problem has a unique solution: (2? - 1.0)y + In (2-1) +(1+1)y" + e*y + (tanrly 22-9 with y(2.5) = A, 7(2.5) B, Y" (2.5) = C, y" (2.5) = D, y(1) (2.5) y (2.5) = F, where A, B, C, D, E, and F are some known constants. E, (b) Determine whether the set of functions {5, sin1, cos 2x} could form a fundamental set of...
(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...
consider the variation of constants formula where P(t)= a) show that solves the initial value problem x'+p(t)=(t) x()= when p and q are continuous functions of t on an interval I and tg p(s)ds We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image tg p(s)ds
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...
Does there exist a unique solution to the following IVP (initial-value-problem) in the neighborhood of the original condition? find all constant solutions. Justify your answers. I am having trouble understanding my professors solution where and . I understand that pi is between 3 and 4 and e is between 2 and 3 but how to you justify that. Also what good does taking the partial derivative of Y have to do with anything, as that also consists of the solution....
Differential equation 1. Chapter 4 covers differential equations of the form an(x)y("4a-,(x)ye-i) + +4(x)y'+4(x)-g(x) Subject to initial conditions y)oyy-Co) Consider the second order differential equation 2x2y" + 5xy, + y-r-x 2- The Existence of a Unique Solution Theorem says there will be a unique solution y(x) to the initial-value problem at x=而over any interval 1 for which the coefficient functions, ai (x) (0 S is n) and g(x) are continuous and a, (x)0. Are there any values of x for...
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
Please help solve this, using the equation to get through the problem. Additional information: where the initial position , the initial speed The above differential equation can also be written as: If , there is light damping where the solution has the form ( where r and w are two positive constants) or If there is heavy damping where, where and are two positive constants If there is critical damping where, where r is a positive constant d'y dy ma...
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...