In Exercises 10-12, you are given a differential equation. The corresponding slope field has also been drawn. Sketch enough solution curves in the slope field to be able to describe the behavior of the family of solutions in the entire (t, x)-plane. As part of your description, explain how the long-term behavior depends on the initial condition x(0). Be as specific as possible. 11. x' + x = t 11 7/11 111

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Chapter2: Second-order Linear Odes
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Chapter 2 First-order Differential Equations
In Exercises 10-12, you are given a differential equation. The corresponding slope field
has also been drawn. Sketch enough solution curves in the slope field to be able to describe
the behavior of the family of solutions in the entire (t, x)-plane. As part of your description,
explain how the long-term behavior depends on the initial condition x(0). Be as specific
as possible.
34
11. x' +x=t
12. x' = t/x
312170
Transcribed Image Text:Chapter 2 First-order Differential Equations In Exercises 10-12, you are given a differential equation. The corresponding slope field has also been drawn. Sketch enough solution curves in the slope field to be able to describe the behavior of the family of solutions in the entire (t, x)-plane. As part of your description, explain how the long-term behavior depends on the initial condition x(0). Be as specific as possible. 34 11. x' +x=t 12. x' = t/x 312170
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