Separable differential equations
Grade 12 Math Worksheet
Circle the best answer, or write your answer on the line.
dy/dx = 2xy² with y(0) = 2. Bo separates and solves. What is y(0.5)?
dy/dx = 2xy² with y(0) = 1. Esme separates and solves. What is y(0.25)?
Cocoa cools by dT/dt = −0.1(T − 20) °C per minute, with T(0) = 90 (example data). Kira separates and solves. What is T(10), to the nearest hundredth?
Cocoa cools by dT/dt = −0.05(T − 25) °C per minute, with T(0) = 85 (example data). Luz separates and solves. What is T(20), to the nearest hundredth?
Cocoa cools by dT/dt = −0.2(T − 15) °C per minute, with T(0) = 75 (example data). Milo separates and solves. What is T(5), to the nearest hundredth?
Cocoa cools by dT/dt = −0.1(T − 22) °C per minute, with T(0) = 100 (example data). Noah separates and solves. What is T(5), to the nearest hundredth?
Pia separates and integrates dy/dx = y cos x. Which is the general solution (C any constant)?
- y = C sin x
- y = Ce^(−sin x)
- y = e^(sin x) + C
- y = Ce^(sin x)
Ren separates and integrates dy/dx = 3x²y. Which is the general solution (C any constant)?
- y = Ce^(−x³)
- y = Cx³
- y = Ce^(x³)
- y = e^(x³) + C
Tala separates and integrates dy/dx = y/x, for x > 0. Which is the general solution (C any constant)?
- y = C ln x
- y = C/x
- y = Cx
- y = x + C
Zee separates and integrates dy/dx = −2xy. Which is the general solution (C any constant)?
- y = Ce^(−x²)
- y = Ce^(x²)
- y = −Cx²
- y = e^(−x²) + C