Track your progress across all skills in your objective. Mark your confidence level and identify areas to focus on.
Track your progress:
Don't know
Working on it
Confident
📖 = included in formula booklet • 🚫 = not in formula booklet
Track your progress:
Don't know
Working on it
Confident
📖 = included in formula booklet • 🚫 = not in formula booklet
Track your progress across all skills in your objective. Mark your confidence level and identify areas to focus on.
Track your progress:
Don't know
Working on it
Confident
📖 = included in formula booklet • 🚫 = not in formula booklet
Track your progress:
Don't know
Working on it
Confident
📖 = included in formula booklet • 🚫 = not in formula booklet
When you have a differential equation in the form
you can bring all the y's to one side and all the x's to the other:
The solutions to differential equations will usually contain a constant of integration +C. These are called general solutions.
Often, we are given an initial condition, ie the value of y for a specific x, which we can use to solve for C. The result is the particular solution.
The easiest differential equations to solve are the ones in the form
as we can simply integrate:
For a differential equation in the form
Multiply both sides by integrating factor (often called μ):
and notice the product rule on the LHS.
Let y=vx, then v=xy​.
Note: On IB exams you will be told to use the substitution y=vx.
Mathematically Euler's Method works as follows:
Start at a known point (x0​,y0​)
Pick a step size h such that x0​+nh=xfinal​ for some integer n.
Repeat the following steps for each n until the desired x-value is reached:
Find the slope dxdy​=f(xn​,yn​)
Find the next x value xn+1​=xn​+h📖.
Find the next y-value yn+1​=yn​+h×f(xn​,yn​)📖