Textbook Question
28. Derivation of Equation (7) in Example 4
a. Show that the solution of the equation
di /dt + R/Li = V/L
is
i = V/R + Cexp(-(R/L)i) .
3
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Ch. 9 - First-Order Differential Equations
Hass15th EditionThomas' CalculusISBN: 9780137616077
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Table of contents
- Ch. 1 - Functions155
- Ch. 2 - Limits and Continuity240
- Ch. 3 - Derivatives337
- Ch. 4 - Applications of Derivatives293
- Ch. 5 - Integrals41
- Ch. 6 - Applications of Definite Integrals25
- Ch. 7 - Transcendental Functions489
- Ch. 8 - Techniques of Integration398
- Ch. 9 - First-Order Differential Equations60
- Ch. 10 - Infinite Sequences and Series119
- Ch. 11 - Parametric Equations and Polar Coordinates58
Chapter 9, Problem 9.2.22a
Solve the following initial value problem for u as a function of t:
du/dt + (k/m) u = 0 (k and m positive constants), u(0) = u₀
a. as a first-order linear equation.
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Related Practice
Textbook Question
Solve the following initial value problem for u as a function of t:
du/dt + (k/m) u = 0 (k and m positive constants), u(0) = u₀
b. as a separable equation.
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Textbook Question
In Exercises 1–22, solve the differential equation.
2y' - y = xe^(x/2)
18
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Textbook Question
In Exercises 23–28, solve the initial value problem.
x dy/dx + 2y = x² + 1, x > 0, y(1) = 1
33
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Textbook Question
In Exercises 23–28, solve the initial value problem.
x dy + (y - cos x) dx = 0, y(π/2) = 0
18
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