Separate variables and use partial fractions to solve the initial value problems in Problems 1-8. Use either the exact solution or a computer-generated slope field to sketch the graphs of sev- eral solutions of the given differential equation, and highlight the indicated particular solution. dx 1. dt dx = x - x², x(0) = 2 2. 10x – x2, x (0) = 1 dt dx dx = 1-x², x(0) = 3 = 9 – 4x2, x(0) = 0 3. 4. dt dt dx Зx (5 — х), х (0) %3 8 dt dx 6. = 3x (x – 5), x (0) = 2 dt dx 7. = 4x(7 – x), x (0) = 11 dt dx 8. 7x(x – 13), x(0) = 17 dt 5.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Separate variables and use partial fractions to solve the initial
value problems in Problems 1-8. Use either the exact solution
or a computer-generated slope field to sketch the graphs of sev-
eral solutions of the given differential equation, and highlight
the indicated particular solution.
dx
1.
dt
dx
= x - x², x(0) = 2 2.
10x – x2, x (0) = 1
dt
dx
dx
= 1-x², x(0) = 3
= 9 – 4x2, x(0) = 0
3.
4.
dt
dt
dx
Зx (5 — х), х (0) %3 8
dt
dx
6.
= 3x (x – 5), x (0) = 2
dt
dx
7.
= 4x(7 – x), x (0) = 11
dt
dx
8.
7x(x – 13), x(0) = 17
dt
5.
Transcribed Image Text:Separate variables and use partial fractions to solve the initial value problems in Problems 1-8. Use either the exact solution or a computer-generated slope field to sketch the graphs of sev- eral solutions of the given differential equation, and highlight the indicated particular solution. dx 1. dt dx = x - x², x(0) = 2 2. 10x – x2, x (0) = 1 dt dx dx = 1-x², x(0) = 3 = 9 – 4x2, x(0) = 0 3. 4. dt dt dx Зx (5 — х), х (0) %3 8 dt dx 6. = 3x (x – 5), x (0) = 2 dt dx 7. = 4x(7 – x), x (0) = 11 dt dx 8. 7x(x – 13), x(0) = 17 dt 5.
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