Given the initial value problem y' + 2xy = 4x , y(0)=3 a) classify the DE by type, order and linearity. b) Give an interval I where the solution is defined and is unique. c) Solve the above IVP

Question.

Given the initial value problem

y' + 2xy = 4x , y(0)=3

a) classify the DE by type, order and linearity.

b) Give an interval I where the solution is defined and is unique.

c) Solve the above IVP

Solution:

Find the largest interval centered about x = 0 for which the IVP has a unique solution y'' - (1/(x^2-1))y = sinx, y(0) = -1, y'(0) = 3

Question. Find the largest interval centered about x = 0 for which the IVP has a unique solution

y'' - (1/(x^2-1))y = sinx, y(0) = -1, y'(0) = 3

Solution: