MATH 240 Midterm: MATH 240 KSU Test 1f98

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

Document Summary

Show all your work in the space provided under each question. Please write neatly and present your answers in an organized way: solve the initial value problem y + 2y = e x y(0) = . 75, find the general solution of the di erential equation dy dx. 2xy2 + 2y + (2x2y + 2x)y = 0. Page 3: consider the initial value problem y = x y y(0) = 2 (a) use the euler method with stepsize . 25 to approximate y(. 5) . Page 4 (b) use the improved euler method with stepsize . 5 to approximate y(. 5) : solve the initial value problem y = x2 cos2 y y(0) = Page 5: a population obeys the equation dp dt. = p (p 10)(p 2) (a) find the equilibrium points of the equation. Clearly mark the axes and the equilibrium solutions. Graph several curves between each set of equilibrium curves. (c) classify each equilibrium point as stable or unstable.