MATH 2065 Study Guide - Final Guide: Integrating Factor, Partial Fraction Decomposition, 2Channel

cos7 x sen x dx = 1/8 cos8 x + c -1/8 sen8 x + c -1/7 cos7 x + c 1/8 sen8 x + c -1/8 cos8 x + c Si y = x2 entonces: y' = 1 + ln(x) y' = 1/x + ln(x) y' = (x ln x) middot x2 y' = (1 + ln x) middot x2 y' = (1/2 ln x) middot x2 Di[le( 2t - 5 / (t + 3)2)] = 2 / 2t - 5 - 2 / t + 3 1 / 2t - 5 + 2 / t + 3 2 / 2t - 5 + 2 / t + 3 1 / 2t - 5 - 2 / t + 3 2 / 2t - 5 - 1 / t + 3 0 1/2 1 / 1 + 4x2 dx -1 pi/6 pi/8 -1/2 ln2 1/2 ln2

The solution of: d^3 y/dt^3 - d^2 y/dt^2 - 2 dy/dt = 0 is a) c_1 = c_2 e^-t + c_3 e^2t b) c_1 + (c_2 + c_3 t)e^t c) c_1 + c_2 e^-t + c_3 e^t d) c_1 + (c_2 + c_3 t)e^-t

The solution of: d^3 y/dt^3 - d^2 y/dt^2 - 2 dy/dt = 0 is a) c_1 + c_2 e^-t + c_3 e^2t b) c_1 + (c_2 + c_3 t)e^t c) c_1 + c_2 e^-t + c_3 e^t d) c_1 + (c_2 + c_3 t)e^-t