Ordinary Differential Equations/First Order Linear 2

how to solve first order linear differential equations

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Return to Exponential Growth Edit

Remember the population growth problem, where

? Now that we can solve linear equations, we can also solve variations where a factor

is added in. The new equation is

, and can be solved by the linear methods taught in the last section.

Immigration Edit

Lets say that 1000 people move into a city, in addition to the normal population growth. This can be interpreted by making

. This gives us a linear differential equation to solve

Step 1: Find

Letting

C=1, we get

Step 2: Multiply through

Step 3: Recognize that the left hand is

Step 5: Solve for y

Hunting Edit

Lets say the government allows 10 animals to be killed a year. This makes

. How does this effect the solution?

Step 1: Find

Letting C=1, we get

Step 2: Multiply through

Step 3: Recognize that the left hand is

Source: en.wikibooks.org

Category: Taxes

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