Overview
Syllabus
Separation of Variables :: dy/dx + 2xy^2 = 0 :: y'+2xy^2=0.
Separation of Variables :: yln(x) dx/dy = ((y+1) /x)^2.
ODE:: y' + 2xy = x^3 :: Integrating Factor.
ODE :: y' - x/(x+1)y = x :: Integrating Factor for Linear Equations.
Exact Equations :: (1-3/y + x) dy/dx +y = 3/x-1.
Exact Differential Equation IVP:: ((y^3-t^2)/y^5)dy/dt = -t/(2y^4).
Linear Models:: Applications of Linear ODEs.
Radius of Convergence for Series Solution of a Differential Equation Including Complex Sing Pts.
ODE:: y'' - xy' + 2y=0 :: Power Series Solution about an Ordinary Point.
What are Regular Singular Points of Differential Equations?? With 3 Full Examples.
ODE :: xy'' + y' +2xy = 0 :: Method of Frobenius Series Solution about a Regular Singular Point.
Show sin(t) y'' + cos(t) y' +n(n+1) sin(t) y = 0 is a Legendre Equation.
The Definition of the Laplace Transform and Three Basic Examples.
Laplace Transform of a Piecewise Function Using the Definition.
Find the Laplace Transform of cos(kt) using the Definition.
Linearity Property of the Laplace Transform and 7 Useful Transforms to Know! Full Example..
Inverse Laplace Transform and Linearity of Inverse Laplace :: With Examples.
Shifting Laplace Transforms :: The First Translation Theorem for Laplace Transforms.
Inverse Laplace Transform :: Completing the Square :: First Translation Theorem in Reverse.
Inverse Laplace Partial Fraction Decomposition :: Overall Strategy.
Use Laplace Transform to Solve Initial Value Problem :: Full Example with Partial Fraction Decomp.
Laplace Transform With Unit Step Functions :: Second Shifting/Translation Theorem.
Proof of the Convolution Theorem :: Laplace Transforms.
Homogeneous System of Linear Differential Equations :: Real Distinct Eigenvalues.
Homogeneous System of Differential Equations :: Complex Eigenvalues.
Bernoulli DIfferential Equation || xy' -(1+x)y = xy^2.
(x^2+2y^2) dx/dy = xy || Homogeneous Substitution.
Taught by
Jonathan Walters