BitWithBite
Mathematics Worksheet
📉 Differential Equations
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Solve dy/dt = ky (exponential growth/decay).Apply an initial condition.Identify the order of an equation.Interpret growth versus decay from k.📚 Quick Recap
A differential equation relates a function to its own rate of change — instead of solving for a number, you solve for an entire function that describes how a system evolves.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1dy/dt = 4y with y(0) = 2 has solution:
2dy/dt = −0.1y, y(0) = 50, at t = 10 gives about:
3The order of dy/dx = x2 + 3 is:
4The order of d3y/dx3 + dy/dx = 2 is:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5dy/dt = ky has solution y = y₀e.
6Negative k gives .
7Solve dy/dt = 4y with y(0) = 2.
8Solve dy/dt = −0.1y with y(0) = 50, and evaluate at t = 10.
9What is the order of dy/dx = x2 + 3?
🚀 Section C · Challenge ● CHALLENGE 5
10What is the order of d3y/dx3 + dy/dx = 2?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 kt 6 decay 7 = y = 2e4t 8 = y = 50e−1 ≈ 18.4 9 = First-order | 10 = Third-order