Finding the general solutions.

Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.

Lesson on Euler's method - used to find general solutions of differential equations.

Intuition and visualization of differential equation solutions using slope fields.

Lesson on solving first order, separable differential equations.

Introduction into finding solutions to differential equations.

Introduction to first order differential equations.

How to get the particular solution to a separable differential equation. Worked example.

Leaving Cert Applied Maths Compound Pendulum Examples. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

The differential equation for the angular position of a compound pendulum for small oscillations is derived from the principle of angular momentum. This has the same form as the differential equation for simple harmonic motion. From this, a formula for the periodic time of the pendulum is found. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

NOTE: Non Leaving Cert Example of a non - separable differential equation. This example shows that a linear combination of the solutions of an ordinary linear differential equation with constant coefficients is itself a solution of the differential equation. This example models a mass attached to a spring in a resistive medium. The force on the mass is proportional to both the displacement and the velocity of the mass. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

In this example, the resistive force on the particle is proportional to the speed v of the particle. Usually the resistive force is proportional to v^2. Because of this resistance, the falling particle reaches a limiting velocity called the terminal velocity. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

A resistive force on a particle always points opposite to the velocity of the particle. Friction is an example of a resistive force. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

Worked solutions to questions on differential equations, as seen on higher level papers 2011 and 2013. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

The order of a differential equation is the order of the highest derivative. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

The order of a differential equation is the order of the highest derivative. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

Calculus is used to explain the formulas for linear motion with uniform acceleration. Derivation of formulas via calculus and differential equations. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug