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# First Order Differential Equations

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2. The solution of the initial value problem (see attachment) is known to exist on -infinite < t <infinite. What is the constant alpha?

3. Let y(t) be a non-constant solution of the differential equation y' + theta*y = 1, where theta is a real number. For what values of theta is lim y(t) finite? What is the limit in this case?

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#### Solution Preview

The equation is:

t dy / dt = 4y = at^2

Or:

dy / dt + 4 / ...

#### Solution Summary

The solution shows in detail how to solve these first order differential equations and how to use a phase diagram to obtain information without the need to solve the equation itself.

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