Differential Equations | IB Math AAHL | Perplex

Differential Equations

Video Reviews

Watch comprehensive video reviews for Differential Equations, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

Not your average video:

Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

Not your average video:

Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

The video will automatically pause when it reaches a problem.

Performing Euler's Method

AHL 5.18

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)📖

Example

Consider the differential equation dxdy=xy. Given that y=1 when x=1, estimate the value of y when x=1.5 using a step size of h=0.25.

We have (x0,y0)=(1,1), and at this point dxdy=11=1.

So x1=x0+h=1.25, and y=y0+h⋅11=1.25. At this point dxdy=1.251.25≈1.32 (using calculator).

So x2=x1+h=1.5 and y2=y1+h⋅1.32≈1.62.

Performing Euler's Method

AHL 5.18

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)📖

Example

Consider the differential equation dxdy=xy. Given that y=1 when x=1, estimate the value of y when x=1.5 using a step size of h=0.25.

We have (x0,y0)=(1,1), and at this point dxdy=11=1.

So x1=x0+h=1.25, and y=y0+h⋅11=1.25. At this point dxdy=1.251.25≈1.32 (using calculator).

So x2=x1+h=1.5 and y2=y1+h⋅1.32≈1.62.