Which is an example of a differential equation?

Example 1 Show that y(x) = x− 3 2 y ( x) = x − 3 2 is a solution to 4x2y′′ +12xy′ +3y = 0 4 x 2 y ″ + 12 x y ′ + 3 y = 0 for x > 0 x > 0 . We’ll need the first and second derivative to do this. Plug these as well as the function into the differential equation.

Where are differential equations taught in Hong Kong?

What follows are my lecture notes for a first course in differential equations, taught at the Hong Kong University of Science and Technology. Included in these notes are links to short tutorial videos posted on YouTube.

What are the initial conditions for a differential equation?

The number of initial conditions that are required for a given differential equation will depend upon the order of the differential equation as we will see. Example 2 y(x) = x−3 2 y ( x) = x − 3 2 is a solution to 4x2y′′ +12xy′ +3y = 0 4 x 2 y ″ + 12 x y ′ + 3 y = 0, y(4) = 1 8 y ( 4) = 1 8, and y′(4) = − 3 64 y ′ ( 4) = − 3 64 .

How are partial differential equations different from Odes?

In contrast to ODEs where there is only one indepen- dent variable, partial differential equations (PDE) contain partial derivatives with respect to more than one independent variable, for instance t (time) and x (a spatial dimension).

https://www.youtube.com/watch?v=NBN1ZtYKGEE

Differential Equations. A Differential Equation is an equation with a function and one or more of its derivatives: Example: an equation with the function y and its derivative dy dx. We solve it when we discover the function y (or set of functions y). There are many “tricks” to solving Differential Equations (if they can be solved!).

How are differential equations used in everyday life?

And how powerful mathematics is! That short equation says “the rate of change of the population over time equals the growth rate times the population”. Differential Equations can describe how populations change, how heat moves, how springs vibrate, how radioactive material decays and much more.

Which is the highest derivative of a differential equation?

The highest derivative is d 3 y/dx 3, but it has no exponent (well actually an exponent of 1 which is not shown), so this is “First Degree”. (The exponent of 2 on dy/dx does not count, as it is not the highest derivative). Be careful not to confuse order with degree. Some people use the word order when they mean degree!

Why is the rate of change a differential equation?

Remember: the bigger the population, the more new rabbits we get! So it is better to say the rate of change (at any instant) is the growth rate times the population at that instant: And that is a Differential Equation, because it has a function N (t) and its derivative. And how powerful mathematics is!