[Solved] MATH 225 Linear Algebra and Differential Equations4

QUESTIONS:

1)(30 pts.)Find the solution of the IVP

with x(0) = 0,y(0) = 1,z(0) = 1.

2)(20 pts.) Find the general solution of the non-homogeneous differential equation y⁽⁴⁾4y⁽³⁾+15y⁰⁰ 22y⁰ +10y = 2cos²x+e^x. Determine the complementary solution y_c and particular solution y_p. DO NOT EVALUATE THE COEFFICIENTS of y_p.

3) (20 pts.) Solve the 2nd order non-homogeneous differential equation x²y⁰⁰ + xy⁰ + y = lnx,x > 0.

IMPORTANT:

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

2.You must show all your work in well-organized English or mathematical sentences, and explain your reasoning carefully.

3.Your project must be hand written. The projects written by latex or word etc. will not be accepted.

4.You must submit your project as a 1 pdf file. Before submission check the file you convert to pdf. If you cannot read it, try to do the best. The name of the pdf file must contain your name. e.g. yosum.project4.pdf would be the name of my project.

5.You must SUBMIT your project. The DRAFTS will not be accepted because DRAFT means INCOMPLETE. You are responsible to complete the submission process. It is not our job. 6. Late submissions will not be accepted