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REMARK Unit step function. 푢(푡 −푎)= {0,푡 < 푎 1,푡 ≥ 푎. Systems of differential equations To solve x0= Ax: x(t) = Ae 1 tv1 + Be 2tv2 + e 3 v3 ( iare your eigenvalues, v i are your eigenvectors) Fundamental matrix: Matrix whose columns are the solutions, without the constants (the columns are solutions and linearly independent) Complex eigenvalues If = g+ i , and v = a + ib. Then: x(t) = A m e tcos( t)a e sin( t)b + B 7 Math 20D, Lecture C00 Midterm II, Cheat Sheet The second order linear, homogeneous, constant-coe cient ODEs are of form ay00+ by0+ cy= 0; which can be solved by considering the characteristic equation 1. Author: Daniel Albert May 25, 2018 www.dennisusa.com 1 Differential Equation and Linear Algebra Exam Review (The Cheat Sheet) Chapter 1: First order linear ODE • Differential equation: A function relationship between that function and its derivative. F (y, y”, y”, y’’’, y’’’’,,,,y (n) ) = 0 • Ordinary differential equation (ODE): differential The formula of differential equation helps in solving differential equation formula sheet.

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Based on Right-click Perform context operation on math expression. Execute list of first order ordinary differential equations or a single.

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