MATH1120 Lecture 6: MATH1120 Week 6

Homework 66: For each of the following first-order DEs, determine whether it is pure-time, autonomous, separable, linear, homogeneous, Bernoulli, or exact. Some of these examples are of more than one type. In many cases you will first need to apply some algebraic transformation to rewrite the DE in the standard form for its type. (g) 2 +/-2x2 (h) ydx + x dy = 0 (0) (x2 + 2) dx (3-Inx2) dy 0) 2 dx yX Department of Mathematics Ohio University -Since 1804 MATH3400, Lecture 30: Solving First-Order DEs Winfried Just, Ohio University

Homework 66: For each of the following first-order DEs determine whether it is pure-time, autonomous, separable, inear, homogeneous, Bernoulli, or exact. Some of these examples are of more than one type. In many cases you will first need to apply some algebraic transformation to rewrite the DE in the standard form for its type.

Problem 5: Using vector fields to understand solutions to DEs. Problem 5: Using vector fields to u (a) Sketch the vector field corresponding to the second order differential equation y" -4y in the y-y-plane. Based on this information, (i) roughly sketch the graph of a solution y(t) in the y-t plane if y(0) = 1 and y'(0) = 0 and finally (ii) try to guess an explicit solution to the equation y"--4y satisfying y(0) = 5. (a) Sketch the vector field corresponding to the second order differential equation y- 2y yin the y-y'-plane. Based on this information, (i) roughly sketch the graplh of a solution y(t) in the y-t plane if y(0) =-3 and y(0) = 2 and finally (ii) try to guess an explicit solution to the equation y"-2y + y, satisfying y(0) = y(1) = 1.