MATH 3D Study Guide - Final Guide: Talking Lifestyle 1278
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Answer: y(ex + ce2x) = 1; y = 0. Find a general solution of the equation y(cid:48) + 2y = y2ex. Answer: y(x) = e x(cid:16) 4 y(cid:48)(cid:48) + 2y(cid:48) + y = 3e x x + 1 (cid:17) Find a general solution of the equation in the domain x (0, ) Solve the initial value problem (cid:26) t, where f(t) = 0 t < 1; t 1. 2 t + 1 x2y(cid:48)(cid:48) xy(cid:48) 3y = 0 (cid:26) y(cid:48) + 2y = f(t) y(0) = 0, Solve the initial value problem for the system of differential equations dt2 + x y = 0 dt2 + y x = 0 x(0) = 0, x(cid:48)(0) = 2, y(0) = 0, y(cid:48)(0) = 1. Answer: y ln(cx) = x; y = 0. Find a general solution of the equation x2y(cid:48) = y(x + y) y(cid:48)(cid:48) 5y(cid:48) = 3x2 + sin 5x.
