<Text-field style="_cstyle1" family="Arial" layout="_pstyle17"><Font family="Arial">Computer project #1 (due to Tuesday, October 2)</Font></Text-field>

The following problems are problems for the first computer project.

<Text-field style="_cstyle2" layout="_pstyle16">Problem 1</Text-field>

Solve 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 , y(0)=1, and plot the solution

<Text-field style="_cstyle2" layout="_pstyle16">Problem 2</Text-field>

Plot the direction field of the equation 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 and solution curves through (0,1) and (0,2)

<Text-field style="_cstyle2" layout="_pstyle16">Problem 3</Text-field>

Is the following equation exact? Find its solution

(x^3+3xy^2)dx+(3x^2 y +y^3)dy=0

<Text-field style="_cstyle2" layout="_pstyle16">Problem 4</Text-field>

Solve the logistic differential equation 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. Find three initial conditions such that the corresponding solutions are (1) increasing, (2) constant, (3) decreasing. Plot these solutions.