MATH 240 Final: MATH 240 KSU Final Exam u05l

• School: Kansas State University
• Department: Mathematics
• Course: MATH 240
• Professor: All

Document Summary

Please show all work. answers with no work will receive non credit. no calculatrs or notes are allowed on this exam. The formula for variation of parameters is: yp = y1(x)z y2(t)g(t) W (y1, y2)(t) dt: (10 pts) solve the following di erential equation: dy dx. 5x 2y y + 2x y(0) = 1: (10 pts) convert 2 2cos(7x) + 2 2sin(7x) to acos( x ), (10 pts) solve the following di erential equation: y . 3 x y = exx4: (10 pts) find the taylor series and radius of convergence for the function f (x) = x. 1 3x: (10 pts) find and classify the equiblibrium points of dp dt. = (p 1. 5)(p 4)p and label the threshold and carrying capacity of this population model: (10 pts) solve the following initial value problem x + 7x . 8x = (t) y(0) = 1; y (0) = 2: (10 pts) find the solution to the boundary value problem x .