In this video I introduce you to the general solutions for the second order linear differential equation

  • a\dfrac{{d^2}y}{d{x^2}} + b\dfrac{dy}{dx} + cy = 0 \hphantom{aa} \text{ where }  a \text{, } b \text{ and } c \text{ are constants}
2nd Order Linear Differential Equations - Auxillary Equation : Introduction : ExamSolutions - youtube Video

Solving equations where b2 – 4ac > 0

In this video I give a worked example of the general solution for the second order linear differential equation which has real and different roots.

Solve the following:

  1. 3\dfrac{{{d^2}y}}{{d{x^2}}} - 4\dfrac{{dy}}{{dx}} + y = 0
2nd Order Linear Differential Equations - Auxillary Equation : Real Different Roots : ExamSolutions - youtube Video

Solving equations where b2 – 4ac = 0

In this video I give a worked example of the general solution for the second order linear differential equation which has real and different roots.

Solve the following:

  1. 4\dfrac{{{d^2}y}}{{d{x^2}}} - 4\dfrac{{dy}}{{dx}} + y = 0
2nd Order Linear Differential Equations - Auxillary Equation : Equal Roots : ExamSolutions - youtube Video

Solving equations where b2 – 4ac < 0

In this video I give a worked example of the general solution for the second order linear differential equation which has imaginary roots.

Solve the following:

  1. \dfrac{{{d^2}y}}{{d{x^2}}} + 2\dfrac{{dy}}{{dx}} + 4y = 0
2nd Order Linear Differential Equations - Auxillary Eqn Imaginary Roots : ExamSolutions - youtube Video