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First-order linear equations practice problems

The integrating factor method for y′ + p(x)y = q(x). 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Solve \( \displaystyle y' + 3y = e^{- 3 x} \) with \( \displaystyle y(0) = 3 \).
Problem 6.24medium✓ Every equation proved
Solve \( \displaystyle y' + 1y = 1 \) with \( \displaystyle y(0) = 0 \).
Problem 6.29medium✓ Every equation proved
Solve \( \displaystyle y' + 2y = 2 \) with \( \displaystyle y(0) = -3 \).
Problem 6.30medium✓ Every equation proved
Solve \( \displaystyle y' + 2y = e^{- 2 x} \) with \( \displaystyle y(0) = 4 \).
Problem 6.62medium✓ Every equation proved
Solve \( \displaystyle y' + 4y = e^{- 4 x} \) with \( \displaystyle y(0) = 0 \).
Problem 6.64medium✓ Every equation proved
Solve \( \displaystyle y' + 1y = 2 e^{x} \) with \( \displaystyle y(0) = -1 \).
Problem 6.69medium✓ Every equation proved
Solve \( \displaystyle y' + 3y = 2 e^{- 3 x} \) with \( \displaystyle y(0) = 1 \).
Problem 6.16hard✓ Every equation proved
Solve \( \displaystyle y' + 3y = e^{x} \) with \( \displaystyle y(0) = 2 \).
Problem 6.17hard✓ Every equation proved
Solve \( \displaystyle y' + 1y = 3 x \) with \( \displaystyle y(0) = -2 \).
Problem 6.18hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = 3 e^{- 4 x} \) with \( \displaystyle y(0) = -1 \).
Problem 6.19hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = 2 x \) with \( \displaystyle y(0) = -2 \).
Problem 6.20hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = 6 \) with \( \displaystyle y(0) = 0 \).
Problem 6.21hard✓ Every equation proved
Solve \( \displaystyle y' + 2y = 2 e^{- 2 x} \) with \( \displaystyle y(0) = 4 \).
Problem 6.22hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = 3 x \) with \( \displaystyle y(0) = -2 \).
Problem 6.23hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = 1 \) with \( \displaystyle y(0) = 3 \).
Problem 6.25hard✓ Every equation proved
Solve \( \displaystyle y' + 2y = 3 e^{- 2 x} \) with \( \displaystyle y(0) = -2 \).
Problem 6.26hard✓ Every equation proved
Solve \( \displaystyle y' + 2y = 2 e^{- 2 x} \) with \( \displaystyle y(0) = 3 \).
Problem 6.27hard✓ Every equation proved
Solve \( \displaystyle y' + 2y = 4 x \) with \( \displaystyle y(0) = 4 \).
Problem 6.28hard✓ Every equation proved
Solve \( \displaystyle y' + 2y = x \) with \( \displaystyle y(0) = 2 \).
Problem 6.61hard✓ Every equation proved
Solve \( \displaystyle y' + 1y = 2 x \) with \( \displaystyle y(0) = 1 \).
Problem 6.63hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = 2 e^{- 4 x} \) with \( \displaystyle y(0) = -2 \).
Problem 6.65hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = e^{x} \) with \( \displaystyle y(0) = 4 \).
Problem 6.66hard✓ Every equation proved
Solve \( \displaystyle y' + 2y = 3 e^{x} \) with \( \displaystyle y(0) = -2 \).
Problem 6.67hard✓ Every equation proved
Solve \( \displaystyle y' + 3y = 1 \) with \( \displaystyle y(0) = 1 \).
Problem 6.68hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = 5 \) with \( \displaystyle y(0) = 3 \).
Problem 6.70hard✓ Every equation proved
Solve \( \displaystyle y' + 3y = 3 e^{x} \) with \( \displaystyle y(0) = -2 \).
Problem 6.71hard✓ Every equation proved
Solve \( \displaystyle y' + 3y = e^{x} \) with \( \displaystyle y(0) = 0 \).
Problem 6.72hard✓ Every equation proved
Solve \( \displaystyle y' + 3y = e^{x} \) with \( \displaystyle y(0) = 1 \).
Problem 6.73hard✓ Every equation proved
Solve \( \displaystyle y' + 4y = 2 e^{x} \) with \( \displaystyle y(0) = 1 \).
Problem 6.74hard✓ Every equation proved
Solve \( \displaystyle y' + 2y = 2 e^{- 2 x} \) with \( \displaystyle y(0) = 1 \).
Problem 6.75hard✓ Every equation proved