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Professor Dave Explains
Power Series Solutions Part 1: Leibniz Method
One technique for solving differential equations is to use power series. Hopefully we remember Maclaurin series and Taylor series from our study of calculus. These will actually have an important application here, as we can use infinite...
Professor Dave Explains
Power Series Solutions Part 2: Frobenius Method
We just learned how to solve differential equations using power series. However the simpler approached we used assumed that all the functions involved are infinitely differentiable at the point we are expanding about. This will not...
Professor Dave Explains
Exact First-Order Differential Equations
We've looked at a few simple examples of first-order differential equations and how to solve them. Now let's take a look at exact first-order differential equations.
Professor Dave Explains
Linear First-Order Differential Equations
We just got our feet wet with separable differential equations, so now let's look at something slightly trickier. Solving linear first-order differential equations will require a little bit more effort, involving something called an...
Khan Academy
Khan Academy: Differential Equations: What Is a Diferential Equation
Video gives an introduction to what differential equations are and shows how they are different from regular equations. Shows an example of a differential equation and how to check if a given answer is a correct solution to a...
Khan Academy
Khan Academy: Differential Equations: Integrating Factors 2
Video continues from previous video showing how to solve the differential equation once the integrating factor is found. [8:26]
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: Laplace Transform to Solve an Equation
Video shows example of using the Laplace transform to solve a differential equation. Problem is continued in next video. [10:51]
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: First Order Homogeneous Equations 2
Video shows an example of using substitution to solve a first order homogeneous differential equation. [8:22]
Khan Academy
Khan Academy: Differential Equations: First Order Homogeneous Equations
Video first shows what homogeneous means in terms of differential equations, then shows how to use substitution to find solutions to the homogeneous differential equation. [7:21]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform to Solve an Equation 2
Video continues from the previous video to show how to use the Laplace transform to solve a differential equation. [10:46]
Khan Academy
Khan Academy: Differential Equations: Exact Equations Example 3
Video shows example of determining if a differential equation is exact and how to solve it. [9:59]
Khan Academy
Khan Academy: Differential Equations: Undetermined Coefficients 2
Video shows an example of solving a second order linear nonhomogeneous differential equation involving trig functions using undetermined coefficients. [11:00]
Khan Academy
Khan Academy: Differential Equations: Undetermined Coefficients 3
Video shows an example of solving a second order linear nonhomogeneous differential equation involving a polynomial function using undetermined coefficients. [8:09]
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: Laplace Transform to Solve Nonhomogeneous
Video shows using the Laplace transform to solve a second order linear nonhomogeneous differential equation. [18:48]
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: Exact Equations Example 1
Video first gives example of determining if an equation is an exact equation and then shows how to solve it. [12:09]
Khan Academy
Khan Academy: Differential Equation: Laplace/step Function Differential Equation
Video demonstrates using the Laplace transform and inverse Laplace transform to solve a differential equation. [19:12]
Khan Academy
Khan Academy: Differential Equations: Convolution Thm for Initial Value Prob
Video shows how the convolution theorem can be used to solve an initial value problem and get it to an integral form. [12:14]
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...