3. Consider the ODE *=-x+², with i.c. z(0) = 10- Determine the time interval of existence of all solutions. Hint: You will need to solve for the solution and the interval should depend on the initial condition zo 4. Given an nonautonomous system of n equations 2-f(z.t) where = (1, 2) ER". Convert this system to an autonomous system of n +1 equations and show that this autonomous system cannot have an equilibrium point.
3. Consider the ODE *=-x+², with i.c. z(0) = 10- Determine the time interval of existence of all solutions. Hint: You will need to solve for the solution and the interval should depend on the initial condition zo 4. Given an nonautonomous system of n equations 2-f(z.t) where = (1, 2) ER". Convert this system to an autonomous system of n +1 equations and show that this autonomous system cannot have an equilibrium point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Consider the ODE
=x+², with i.c. 2(0) = zo.
Determine the time interval of existence of all solutions. Hint: You will need to solve for the
solution and the interval should depend on the initial condition ro
4. Given an nonautonomous system of n equations
#= f(z.t)
where - (1,22₂...) ER". Convert this system to an autonomous system of n + 1
equations and show that this autonomous system cannot have an equilibrium point.
71°F Mostly clea
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