First order differential equations

This course is a part of Differential equations, a 3-course Topic series from Khan Academy.

Differential equations with only first derivatives.

This course contains 8 segments:

Intro to differential equations

How is a differential equation different from a regular one? Well, the solution is a function (or a class of functions), not a number. How do you like me now (that is what the differential equation would say in response to your shock)!

Slope fields

Slope fields are a tool we can use to analyze differential equations graphically. They don't demand any elaborate algebraic tool, which makes them easy to use.

Euler's Method

Euler's method is a relatively simple numerical tool for approximating values for solutions of differential equations. It is based on the understanding that a function behaves similar to its tangent around the point where the tangent touches the function.

Separable equations

Arguably the 'easiest' class of differential equations. Here we use our powers of algebra to "separate" the y's from the x's on two different sides of the equation and then we just integrate!

Exponential models

Exponential functions are described by differential equations of the general form dy/dx=ky, i.e. equations where the derivative is proportional to the function. Learn how to solve such equations and how to solve word problems with real-world contexts involving such equations.

Logistic models

Can population grow exponentially forever? Malthus would say "no". Well how do you model that mathematically. The logistic differential equation and logistic function are there to rescue us!

Exact equations and integrating factors

A very special class of often non-linear differential equations. If you know a bit about partial derivatives, this tutorial will help you know how to 'exactly' solve these!

Homogeneous equations

In this equations, all of the fat is fully mixed in so it doesn't collect at the top. No (that would be homogenized equations). Actually, the term "homogeneous" is way overused in differential equations. In this tutorial, we'll look at equations of the form y'=(F(y/x)).