Homogeneous linear second order differential equations

Intros
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Lessons
  1. What are Homogeneous Linear Second Order Differential Equations? And what are some sorts of solutions to them?
  2. What is the Characteristic Equation?
Examples
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Lessons
  1. Solving Homogeneous Linear Second Order Differential Equations
    Find some general solutions to the following constant coefficient homogeneous linear second order differential equation:

    2y′′+5y′−3y=02y''+5y'-3y=0
  2. Using the initial conditions find a particular solution to the following differential equation:

    y′′+3y′−4y=0y''+3y'-4y=0
    y(0)=3,y′(0)=−2y(0)=3, y' (0)=-2