MATH 240 Midterm: Kansas State MATH 240 exam1sum09

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

Document Summary

You must show all your work to receive credit. (10) 1. Find all solutions of the di erential equation (implicit form is accepted) Find all solutions to the equation dy dx. Find all solutions to the equation dy dx y. Solve the initial value problem dy dx y2 + 4x2. Find all solutions to the equation x dy dx. Write the expression in the form a + bi, where a and b are real numbers: (a) 1 3i (b) (1 i)20 (hint: use exponential form) 6 (10) 7. (a) express in the form a cos( x ): sin(3x) . 3 cos(3x) (b) express in the form a cos( x) + b sin( x): Suppose that population of bisons in konza prairie satis es the di erential equation dp dt. = 0. 1 p (p 300)(p 100) (a) find the equilibrium points of the equation. Sketch several trajectories, including equilibrium solutions. (b) assume current population is equal to 85 bisons.