Question

Find an interval I for which the given IVP is guaranteed to have a unique solution....

Find an interval I for which the given IVP is guaranteed to have a unique solution.

(x-1) y''- [y'/(x-4)] +(x-3)y=0, y(2)=0, y' (2)=1

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Differential Equation :

y(2)=0, y'(2)=1

f1(x) and f2(x) must be continuous in the largest interval for given IVP to have unique solution.

is discontinuous at x = 1 and 4

and

is discontinuous at x = 1.

Therefore largest interval containing initial value x =2 having unique solution is [1 , 4]

1 and 4 are in close interval, it also contain x =2 and there is no discontinuity between x = 1 to 4.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use the Existence and Uniqueness Theorem to find the maximum interval for the existing unique solution...
Use the Existence and Uniqueness Theorem to find the maximum interval for the existing unique solution for this IVP: ((x^2)-9)y' + (x + 3)y = cosx and y(0) = 0
9) Find the maximal interval of existence, I, for each IVP given. A) (t^2 − 9)...
9) Find the maximal interval of existence, I, for each IVP given. A) (t^2 − 9) y′ − 7t^3 =√t, y(−2) = 12 B) sin(t) y′′ + ty′ − 18y = 1, y(4) = 9, y′(4) = −13
consider ivp given by x^2y" + 2xy' - 6y = 0 w/ y(1) = 1, y'(1)...
consider ivp given by x^2y" + 2xy' - 6y = 0 w/ y(1) = 1, y'(1) = 2 verify y(x) = x^2 and y(x) = x^-3 are solutions use wronskian to show both y(x) above are linearly independent find unique solution to ivp
10. Find the solution of the given initial value problem. State the largest interval in which...
10. Find the solution of the given initial value problem. State the largest interval in which the solution is guaranteed to uniquely exist. ty′′− y′ = t^2 +t, y(1)=1, y′(1)=5.
According to the Existence and Uniqueness Theorem, which of the following differential equations are guaranteed to...
According to the Existence and Uniqueness Theorem, which of the following differential equations are guaranteed to have a unique solution on the specified interval. Explain your reasoning (3x)(d^2y/dx^2)-5(dy/dx)+y=e^x y(0)=-1,, y(1)=2
Given the IVP x * sqrt(x+1) * y'''-y'+xy=0 when y(1/2)=y'(1/2)=-1 , and y''(1/2)=1 determine the larest...
Given the IVP x * sqrt(x+1) * y'''-y'+xy=0 when y(1/2)=y'(1/2)=-1 , and y''(1/2)=1 determine the larest interval for which the apporpriate existsence and uniqueness therom gaurentees the exsistence of a unique solution, show all work and fully justify why andhow you got that interval.
According to the Existence and Uniqueness Theorem, which of the following differential equations are guaranteed to...
According to the Existence and Uniqueness Theorem, which of the following differential equations are guaranteed to have a unique solution on the specified interval. Explain your reasoning. x2d3ydx3-4x-1d2ydx2+3dydx+2y=0,y″(0)=2,y'(0)=1,y(0)=0
Are both of the following IVPs guaranteed a unique solution? Explain. (a) dy/dt =y^ 1/3sin(t), y(π/2)=0....
Are both of the following IVPs guaranteed a unique solution? Explain. (a) dy/dt =y^ 1/3sin(t), y(π/2)=0. (b) dy/dt =y^1/3 sin(t), y(π/2)=4.
determine if the xy-plane for which the given differential equation would have a unique solution whose...
determine if the xy-plane for which the given differential equation would have a unique solution whose graph passes through the point (x0,y0) in the region dy/dx=y^(2/3) x(dy/dx)=y
Consider the following Initial Value Problem (IVP) y' = 2xy, y(0) = 1. Does the IVP...
Consider the following Initial Value Problem (IVP) y' = 2xy, y(0) = 1. Does the IVP exists unique solution? Why? If it does, find the solution by Picard iteration with y0(x) = 1.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT