State the longest interval, if any, in which the given IVP is certain to have a...
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. Determine the longest interval in which the initial value problem below is certain to have a unique twice- differentiable solution. ty"+3y 0 y(1) 1 (1) = 2 Explain your reasoning.
6. Please help me solve the following Differential Equations question. please show work. Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not a solution. (Enter your answer using interval notation.) t E 匝 Show My Work@ptionali@
Chapter 3, Section 3.2, Additional Go Tutorial Problem 02 11 Determine the longest interval in which the initial value problem is certain to have a unique twice differentiable solution. (Do not attempt to find the solution.) (1-2))" - 217 +10y = sin , (-9) = 9, 7(-9) = 2 Type "in" for + and "-int" for -- N
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
(Q3) Consider the equation: y′ = y1/3, y(0) = 0 . (a)Does the above IVP have any solution? (b)Is the solution unique? (c)Interpret your results in light of the theorem of existence and uniqueness. (Q3) Consider the equation: y' = y1/3, y(0) = 0 . (a)Does the above IVP have any solution? (b) Is the solution unique? (c)Interpret your results in light of the theorem of existence and uniqueness. (Q4) Solve the following IVP and find the interval of validity:...
Section 3.2 The Wronskian: Problem 5 Previous Problem Problem List Next Problem (1 point) Determine the largest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution. d2x sin(t)atx + cos(r)ar + sin(,)x = tan(t), dx x(0.5)-8, x,(0.5)-10 Interval Section 3.2 The Wronskian: Problem 5 Previous Problem Problem List Next Problem (1 point) Determine the largest interval in which the given initial value problem is certain to...
please help Fundamental Existence Theorem for Linear Differential Equations Given an IVP d"y d" y dy +ao(x)ygx) dx ... a1 (x)- + an-1 (x) dx" а, (х) dx"-1 yу-D (хо) — Уп-1 У(хо) %3D Уо, у (хо) — У1, ..., If the coefficients a,(x), ... , ao(x) and the right hand side of the equation g(x) are continuous on an interval I and if a,(x) 0 on I then the IVP has a unique solution for the point xo E...
differential equation Convert the IVP into an IVP for a system in normal ( canonical) form: y(+y(O-340=t; x0- 3; y(o = -6 a) b.) Given F(s)= - . Find (f f)( dv= J Solve the integral equation: c) Solve the IVP using Laplace transforms: d.) ty+y-y-O,XO) = 0; y(0) =1 Convert the IVP into an IVP for a system in normal ( canonical) form: y(+y(O-340=t; x0- 3; y(o = -6 a) b.) Given F(s)= - . Find (f f)( dv=...