Textbook Question
First-Order Linear Equations
Solve the differential equations in Exercises 1–14.
(t-1)³ ds/dt + 4(t-1)²s = t+1, t >1
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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 9.1.23
Use Euler’s method with dx = 0.5 to estimate y(5) if y′ = y²/√x and y(1) = −1. What is the exact value of y(5)?
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Related Practice
Textbook Question
Solving Initial Value Problems
Solve the initial value problems in Exercises 15–20.
t dy/dt + 2y = t³, t > 0, y(2) = 1
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Textbook Question
Solve the Bernoulli equations in Exercises 29–32.
x²y' + 2xy = y³
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Textbook Question
Show that the solution of the initial value problem
y' = x + y, y(x₀) = y₀
is
y = -1 -x + (1 + x₀ + y₀) exp(x-x₀).
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Textbook Question
First-Order Linear Equations
Solve the differential equations in Exercises 1–14.
xdy/dx + y = e ͯ, x > 0
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Textbook Question
Solving Initial Value Problems
Solve the initial value problems in Exercises 15–20.
dy/dt + 2y = 3, y(0) = 1
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