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Question

# A family of solutions includes solutions to a differential equation that differ by a constant. For the following problem, use your calculator to graph a family of solutions to the given differential equation. Use initial conditions from y(t = 0) = −10 to y(t = 0) = 10 increasing by 2. Is there some critical point where the behavior of the solution begins to change? [T] y’ = x + y

Solution

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Mathematica code::Sols = Table[  DSolve[{y'[x] == x + y[x], y[0] == j}, y[x], x], {j, -10, 10, 2}]Plot[Evaluate[y[x] /. Sols], {x, -5, 5}, PlotRange -> {-10, 10},  PlotLegends -> "Expressions"]

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