Separable differential equations

Answer Key - Grade 12 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   dy/dx = 2xy² with y(0) = 1. Ari separates and solves. What is y(0.5)?

   4/3
2. 2.

   dy/dx = 2xy² with y(0) = 1. Esme separates and solves. What is y(0.25)?

   16/15
3. 3.

   dy/dx = 2xy² with y(0) = 4. Jun separates and solves. What is y(0.25)?

   16/3
4. 4.

   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?

   45.75
5. 5.

   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?

   37.07
6. 6.

   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?

   69.31
7. 7.

   Pia separates and integrates dy/dx = y cos x. Which is the general solution (C any constant)?

   • y = e^(sin x) + C
   • y = C sin x
   • y = Ce^(sin x)
   • y = Ce^(−sin x)
8. 8.

   Ren separates and integrates dy/dx = 3x²y. Which is the general solution (C any constant)?

   • y = e^(x³) + C
   • y = Ce^(−x³)
   • y = Ce^(x³)
   • y = Cx³
9. 9.

   Tala separates and integrates dy/dx = y/x, for x > 0. Which is the general solution (C any constant)?

   • y = C/x
   • y = Cx
   • y = C ln x
   • y = x + C
10. 10.

    Zee separates and integrates dy/dx = −2xy. Which is the general solution (C any constant)?

    • y = −Cx²
    • y = Ce^(x²)
    • y = Ce^(−x²)
    • y = e^(−x²) + C