[Solved] MATH 225 Linear Algebra and Differential Equations

QUESTIONS:

1)In each of the following, decide if the Existence and Uniqueness Theorem is applicable. Find, if exists, the solution(s) for each of items.

(a)(15 pts.)y⁰ = 5y^4/5, y(0) = 0.

(b)(15 pts.) y⁰ = 5y^4/5, y(0) = 1.

• (a)(10 pts.) Find the continuous solution to the initial value problem dy1 if |x| 1

+ y = q(x) where q( ) = satisfying y(0) = 0.

_dx0 if |x| > 1

(b)(10 pts.)Solve the differential equation

• Let (3xy y²)dx + x(x y)dy = 0 be given.

(a)(5 pts.) Show that the given equation is not exact.

(a)(15 pts.) Find an integrating factor which makes the given equation exact and solve it as an exact differential equation.

IMPORTANT:

1.Dont forget to write your Name, Lastname, Department, Section and Student ID on the 1st page of your project.

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