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- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/10%3A_Linear_Systems_of_Differential_Equations/10.02%3A_Linear_Systems_of_Differential_EquationsA first order system of differential equations are introduced.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/10%3A_Linear_Systems_of_Differential_Equations/10.02%3A_Linear_Systems_of_Differential_EquationsA first order system of differential equations are introduced.
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_2562_Differential_Equations_with_Linear_Algebra/10%3A_Linear_Systems_of_Differential_Equations/10.02%3A_Linear_Systems_of_Differential_EquationsA first order system of differential equations are introduced.
- https://math.libretexts.org/Courses/Chabot_College/Math_4%3A_Differential_Equations_(Dinh)/04%3A_Linear_Higher_Order_Differential__Equations/4.01%3A_Second_Order_Homogeneous_Linear_EquationsThis section is devoted to the theory of homogeneous linear equations.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/05%3A_Linear_Second_Order_Equations/5.01%3A_Homogeneous_Linear_EquationsThis section is devoted to the theory of homogeneous linear equations.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_420%3A_Differential_Equations_(Breitenbach)/10%3A_Linear_Systems_of_Differential_Equations/01%3A_Linear_Systems_of_Differential_Equations\( \newcommand{\place}{\bigskip\hrule\bigskip\noindent} \newcommand{\threecol}[3]{\left[\boldsymbol{\begin{array}{r}#1\\#2\\#3\end{array}}\right]} \newcommand{\threecolj}[3]{\left[\begin{array}{r}#1\\[1\jot]#2\\[1...\( \newcommand{\place}{\bigskip\hrule\bigskip\noindent} \newcommand{\threecol}[3]{\left[\boldsymbol{\begin{array}{r}#1\\#2\\#3\end{array}}\right]} \newcommand{\threecolj}[3]{\left[\boldsymbol{\begin{array}{r}#1\\[1\jot]#2\\[1\jot]#3\end{array}}\right]} \newcommand{\lims}[2]{\,\bigg|_{#1}^{#2}} \newcommand{\twocol}[2]{\left[\boldsymbol{\begin{array}{l}#1\\#2\end{array}}\right]} \newcommand{\ctwocol}[2]{\left[\boldsymbol{\begin{array}{c}#1\\#2\end{array}}\right]} \newcommand{\cthreecol}[3]{\left[\boldsymbol{\begin{array}{c}#1\\#2\\#3\end{array}}\right]} \newco…
- https://math.libretexts.org/Under_Construction/Purgatory/Differential_Equations_and_Linear_Algebra_(Zook)/20%3A_Linear_Systems_of_Differential_Equations/20.02%3A_Linear_Systems_of_Differential_EquationsA first order system of differential equations are introduced.
- https://math.libretexts.org/Under_Construction/Purgatory/Differential_Equations_and_Linear_Algebra_(Zook)/04%3A_Linear_Second_Order_Equations/4.01%3A_Homogeneous_Linear_EquationsThis section is devoted to the theory of homogeneous linear equations.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_420%3A_Differential_Equations_(Breitenbach)/05%3A_Linear_Second_Order_Equations/5.01%3A_Homogeneous_Linear_EquationsRemember that a solution of an initial value problem is defined on an interval that contains the initial point; therefore, the solution of Equation ??? is y=x2+1/x2 on the interval \...Remember that a solution of an initial value problem is defined on an interval that contains the initial point; therefore, the solution of Equation ??? is y=x2+1/x2 on the interval (0,∞), which contains the initial point x0=1, while the solution of Equation ??? is y=x2+1/x2 on the interval (−∞,0), which contains the initial point x0=−1.
- https://math.libretexts.org/Courses/Mt._San_Jacinto_College/Differential_Equations_(No_Linear_Algebra_Required)/04%3A__Higher_Order_Linear_ODEs/4.01%3A_Homogeneous_Linear_Second_Order_EquationsIf y=c1cosωx+c2sinωx then y′=ω(−c1sinωx+c2cosωx) and y″=−ω2(c1cosωx+c2sinωx), so...If \boldsymbol{\label{eq:5.1.10} y=c_1\cos\omega x+c_2\sin\omega x} then \boldsymbol{\label{eq:5.1.11} y'=\omega(-c_1\sin\omega x+c_2\cos\omega x)} and y″=−ω2(c1cosωx+c2sinωx), so y″+ω2y=−ω2(c1cosωx+c2sinωx)+ω2(c1cosωx+c2sinωx)=c1ω2(−cosωx+cosωx)+c2ω2(−sinωx+sinωx)=0 for all x.
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_2562_Differential_Equations_with_Linear_Algebra/05%3A_Linear_Second_Order_Equations/5.01%3A_Homogeneous_Linear_EquationsThis section is devoted to the theory of homogeneous linear equations.
