Separable differential equations

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   dy/dx = e^(x − y) with y(0) = ln 2. Ari writes it as eʸ dy = eˣ dx and solves. What is y(1), to the nearest hundredth?

   1.31
2. 2.

   dy/dx = e^(x − y) with y(0) = ln 3. Bo writes it as eʸ dy = eˣ dx and solves. What is y(1), to the nearest hundredth?

   1.55
3. 3.

   dy/dx = e^(x − y) with y(0) = ln 5. Esme writes it as eʸ dy = eˣ dx and solves. What is y(2), to the nearest hundredth?

   2.43
4. 4.

   A sprout count follows dy/dt = ky (example data): 100 at t = 0, 400 at t = 3. What does Kira find it is at t = 6?

   1600
5. 5.

   A fund in dollars follows dy/dt = ky (example data): 50 at t = 0, 150 at t = 2. What does Luz find it is at t = 4?

   450
6. 6.

   A solar panel count follows dy/dt = ky (example data): 20 at t = 0, 60 at t = 5. What does Milo find it is at t = 15?

   540
7. 7.

   Dye in grams follows dy/dt = ky (example data): 80 at t = 0, 40 at t = 1. What does Noah find it is at t = 3?

   10
8. 8.

   dy/dx = cos x / y with y(0) = 2 and y > 0. Pia separates and solves. What is y(π/2), to the nearest hundredth?

   2.45
9. 9.

   dy/dx = cos x / y with y(0) = 1 and y > 0. Tala separates and solves. What is y(π/2), to the nearest hundredth?

   1.73
10. 10.

    dy/dx = cos x / y with y(0) = 4 and y > 0. Zee separates and solves. What is y(π/6), to the nearest hundredth?

    4.12