4.1 to 4.3 Higher-Order Differential Equations

What is a higher-order differential equation

• when there is a function that is like $y^n+p_{n-1}t{y}^{n-1}\dots$ so its like more y''''''' y’know

  • the general solution will involve n arbitrary constants that can be determined by applying n initial conditions

Existance and uniqueness

• what

• Similarities with seconed order ODE’s

  • a 3.1 Second-order homogeneous Differential Equations has the form

    • $y^n+p_{n-1}(t)y^{n-1}+\cdots +p_1(t)y^{\prime }+p_0(t)y=0$

  • b) super position principle: if $y_1,y_2\dots y_n$ are solutions of ODE then any linear combinitaion

    • $y(t)=c_1{y}_1(t)+c_2{y}_2(t)+\cdots +c_n{y}_n(t)$

  • c) wronkian condition substituting the initial … (Laplase)