MATH 302 Section: 010; Spring 2022
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MATH 302 Section: 010; Spring 2022
Homework 1
1. For the differential equation given by y′ + 3y = t + e −2t, answer the following questions.
(a) What is the integrating factor?
(b) What is the general solution?
(c) From the general solution you found in part (c), determine how the solutions behave as t → ∞ .
(d) What is the stationary solution of the given differential equation?
2. For the differential equation y′ + y = 3cos(2t) for t > 0, answer the following questions.
(a) What is the integrating factor?
(b) What is the general solution?
(c) What is the stationary solution?
3. For the differential equation y′ + y = for t > 0, answer the following questions.
(a) What is the integrating factor?
(b) What is the general solution?
(c) What is the solution given that y(π) = 0?
4. Find the solution to the initial value problem y′ − y = 2te2t , y(0) = 1 and find the value of y(0.5).
5. Find the general solution to 2y′ + ty = 2 and find lim y .
6. Show that if a and λ are positive constants, and b is any real number, then every solution to y′ + ay = be −λt has the property y → 0 as t → ∞ . [Hint: Consider the cases a = λ and a λ separately.]
2022-02-15