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!
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!
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.
Differential_equations_introduction
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)!
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.
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.
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