Grade 12 · Math · Calculus

12th grade Separable differential equations worksheet

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Separable differential equations

Grade 12 Math Worksheet - Building Confidence

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

1.
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
2.
Esme separates dy/dx = y/x² so that all y's are with dy and all x's with dx. Which is right?
- y dy = dx/x²
- dy/y = x² dx
- y = −y/x + C
- dy/y = dx/x²
3.
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
- dy/y² = dx/(x + 1)
- y = (x²/2 + x)y² + C
- dy/y² = (x + 1) dx
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?
An account balance in dollars follows dy/dt = 0.2y with y(0) = 50 (example data). Luz separates and solves. What is y(5), to the nearest hundredth?
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?
A savings fund in dollars follows dy/dt = 0.1y with y(0) = 200 (example data). Noah separates and solves. What is y(3), to the nearest hundredth?
dy/dx = x/y with y(0) = 3. Pia separates, integrates and uses the start. What is y(4)?
dy/dx = x/y with y(0) = 5. Ren separates, integrates and uses the start. What is y(12)?
dy/dx = x/y with y(0) = 6. Tala separates, integrates and uses the start. What is y(8)?

Separable differential equations. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

separable: dy/dx = (x-part) × (y-part).

general solution: All the solutions, with a constant C.

dy/dt = ky: Growth or decay at a rate proportional to the amount.

Moved the y-factor to the dy side the wrong way: a factor that multiplies on one side divides on the other.

Changed the x-factor while separating. Only the y's move.

Integrated in x while y was still on the right. Separate first.

What is the most common mistake with separable differential equations?

Moved the y-factor to the dy side the wrong way: a factor that multiplies on one side divides on the other.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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