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Khan Academy
Khan Academy: Differential Equations: 2nd Order Linear Homogeneous Equations 4
Video shows using the foundation shown in previous videos how to more quickly find a solution to a second order linear homogeneous differential equation. Includes using initial conditions with the general solution to find a particular...
Khan Academy
Khan Academy: Differential Equations: Complex Roots of Characteristic Equation 1
Video is first part of showing what happens in a secondnd order linear homogeneous differential equation when the roots of the characteristic equation are complex. Includes using Euler's formula. [10:27]
Khan Academy
Khan Academy: Differential Equations: Complex Roots of Characteristic Equation 2
Video continues from previous video showing what happens when the roots of the characteristic equation are complex and deriving a formula for the general solution. Shows an example problem applying the formula derived to determine the...
Khan Academy
Khan Academy: Differential Equations: Repeated Roots of Characteristic Equations
Video shows what happens when the characteristic equation has repeated roots. Explains why just using the one root will not give a correct general equation. Shows an example of solving a differential equation where the characteristic...
Khan Academy
Khan Academy: Differential Equations: Complex Roots of Characteristic Equation 3
Video shows example of using formula derived in previous video for general solution of a differential equation when characteristic equation has complex roots. Includes using initial conditions to determine a particular solution. Shows...
Khan Academy
Khan Academy: Differential Equations: 2nd Order Linear Homogeneous Equations 2
Video shows an example of solving a second order linear homogeneous differential equation. Includes how to write the solution in a general form using the properties of homogeneous equations shown in the previous video. Briefly discusses...
Khan Academy
Khan Academy: Differential Equations: 2nd Order Linear Homogeneous Equations 1
Video first explains what 2nd order linear differential equations are, then shows that a constant times a known solution to a 2nd order linear homogenous differential equation is also a solution and that the sum of two known solutions is...
Khan Academy
Khan Academy: Differential Equations: 2nd Order Linear Homogeneous Equations 3
Video continues from previous video where a general solution to a secondnd order linear homogeneous differential equation was found. Extends showing how to use initial conditions to find a particular solution. [5:59]
Khan Academy
Khan Academy: Differential Equations:repeated Roots of Characteristic Equation 2
Video shows example of solving a second order linear homogeneous differential equation when the characteristic equation has repeated roots. Includes using initial conditions to find a particular solution. [8:52]
Khan Academy
Khan Academy: Second Order Linear Homogeneous Differential Equations 3
This video shows how to use some initial conditions to solve for a particular solution.