Separable differential equations

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari separates dy/dx = x/y so that all y's are with dy and all x's with dx. Which is right?

   • dy/y = x dx
   • y = x²/(2y) + C
   • y dy = x dx
   • y dy = dx/x
2. 2.

   Bo separates dy/dx = xy so that all y's are with dy and all x's with dx. Which is right?

   • dy/y = dx/x
   • y dy = x dx
   • dy/y = x dx
   • y = x²y/2 + C
3. 3.

   Esme separates dy/dx = y/x² so that all y's are with dy and all x's with dx. Which is right?

   • dy/y = dx/x²
   • y = −y/x + C
   • y dy = dx/x²
   • dy/y = x² dx
4. 4.

   Jun separates dy/dx = (x + 1)y² so that all y's are with dy and all x's with dx. Which is right?

   • y² dy = (x + 1) dx
   • y = (x²/2 + x)y² + C
   • dy/y² = (x + 1) dx
   • dy/y² = dx/(x + 1)
5. 5.

   A seed tray's sprout count follows dy/dt = 0.5y with y(0) = 10 (example data). Kira separates and solves. What is y(2), to the nearest hundredth?

   27.18
6. 6.

   Dye left in a tank, in grams follows dy/dt = -0.3y with y(0) = 80 (example data). Milo separates and solves. What is y(2), to the nearest hundredth?

   43.9
7. 7.

   dy/dx = x/y with y(0) = 3. Pia separates, integrates and uses the start. What is y(4)?

   5
8. 8.

   dy/dx = x/y with y(0) = 5. Ren separates, integrates and uses the start. What is y(12)?

   13
9. 9.

   dy/dx = x/y with y(0) = 6. Tala separates, integrates and uses the start. What is y(8)?

   10
10. 10.

    dy/dx = x/y with y(0) = 8. Zee separates, integrates and uses the start. What is y(15)?

    17