*ds*/

*dt*=1.5

*s*(where

*s*is the daisy population). Using this differential equation, find the population growth equation for daisies.

Differential Equations Flashcards

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Solve the following:

The solution is:

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Solve for the following for *y*:

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Separation of Variables

Technique used to solve differential equations that involves isolating variables to their own sides of the equation. For example, only having *x* on one side of the equation and *y* on the other.

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Solve the following for *y*:

The solution is:

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Solve the following:

The solution is:

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Suppose the population of daisies in a field increases at the rate: *ds*/*dt*=1.5*s* (where *s* is the daisy population). Using this differential equation, find the population growth equation for daisies.

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Math 104: Calculus Formulas & Properties

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Use this differential equations flashcard set to help you brush up on your calculus skills. Differential equations can be a difficult topic to master, but this flashcard set breaks down the fundamentals of what's involved when solving these equations. Techniques like separation of variables and differential notation are discussed, as well as more difficult application problems involving related rates. Use this flashcard set to study for your next calculus test or to ensure mastery of differential equations.

To learn more about differential equations, check out these lessons:

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Solve the following:

The solution is:

Solve the following for *y*:

The solution is:

Separation of Variables

Technique used to solve differential equations that involves isolating variables to their own sides of the equation. For example, only having *x* on one side of the equation and *y* on the other.

Solve for the following for *y*:

Solve the following:

The solution is:

A cylindrical pool drains at a constant rate of *dV*/*dt* = 600 cm3/sec. Solve for how fast the height of the pool will change (*dh*/*dt*) if the pool has a radius of 500 cm. (*V* = *pi***r* 2**h*)

Related Rate Problems

These problems involve finding the rate of change of a quantity by relating that rate to other known rates. A common related rate problem is the draining tank problem.

Distance Formula

The distance formula is:

The equation for a line is *y* = *x*3 + 3 and the *x*-coordinate is increasing at a rate of 1 unit/sec. When the point is (1,4), find the rate that the points distance from the origin is changing.

The rate (in units/sec) is:

Differential Equation

Differential equations relate a function to its derivative. In other words, it relates a function (and variables) to a rate of change.

Determine if the following is a differential equation.

No, this is not a differential equation. A differential equation must relate a variable to a rate of change.

Determine if the following is a differential equation.

Yes, this is a differential equation because it relates a variable and its rate of change.

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Math 104: Calculus16 chapters | 135 lessons | 11 flashcard sets

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- Graphing Functions Flashcards
- Function Continuity Flashcards
- Geometry & Trigonometry Flashcards
- Limits in Calculus Flashcards
- Rate of Change in Calculus Flashcards
- Solving Derivatives Flashcards
- Graphing Derivatives & L'Hopital's Rule Flashcards
- Applications of Derivatives Flashcards
- Integrals & the Area Under the Curve Flashcards
- Integration in Calculus Flashcards
- Differential Equations Flashcards
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