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The rate of growth of the population, assuming that the rate of growth of the population is proportional to the population size is:
 - P'(t)=kP
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The solution for the following differential equation:
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Another way to write the solution for the following equation, when M (carrying capacity) is considered
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A separable differential equation dy/dx can be re-written as:
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Differential equation to model current in an electric circuit:
- L= inductance(H)
- I= current(amperes)
- R= resistance(Ω)
- t= time(s)
- E=energy/voltage(V)
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Differential equation used in "mixing problems"
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Equation for the law of natural growth:
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The equation for the law of natural growth is . Solve the differentiable equation.
- e^C= A
- A=initial population
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Differential equation modeling population growth and carrying capacity, also known as a logistic differential equation:
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Solve the differential logistic growth equation
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Solution for the differential logistic growth equation
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In the following equation, what does A represent?
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The form of a first order, linear, differential equation:
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What is the integration factor?
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- We try to find so that the left side, when multiplied by I(x), becomes the derivative of the product
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Another format for the integration factor:
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Newton's law of cooling. Solve for the differential equation
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Area for:
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Arc length for a parametric equation
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Surface area for a parametric around the x-axis
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To find the Cartesian coordinates (x,y) when the polar coordinates (r,θ) are known:
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To find the polar coordinates (r,θ) when the Cartesian coordinates (x,y) are known:
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Slope formula for polar coordinates
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Length of a curve in polar coordinates
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Basic form of a first order linear differential equation (that cannot be separated)
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