Content
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​)📖​