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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

Description:

Explore a comprehensive 3-hour 30-minute tutorial on differential equations, covering a wide range of topics and techniques. Begin with separation of variables and integrating factors for solving ordinary differential equations (ODEs). Progress through exact equations, linear models, and applications of linear ODEs. Delve into advanced concepts such as series solutions, regular singular points, and the method of Frobenius. Study the Legendre equation and its properties. Master the Laplace transform, including its definition, linearity properties, and inverse transformations. Learn to solve initial value problems using Laplace transforms and unit step functions. Examine systems of linear differential equations with real and complex eigenvalues. Conclude with specialized equation types like Bernoulli and homogeneous differential equations. Gain practical problem-solving skills through numerous examples and full solutions throughout the tutorial.

Differential Equations

Jonathan Walters

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#Mathematics #Differential Equations #Mathematical Analysis #Laplace Transform #Computer Science #Machine Learning #Linear Models #Separation of Variables #Integrating Factors

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