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Undetermined coefficients practice problems

y″ + py′ + qy = g(x): solve the homogeneous equation, guess the form of a particular solution, and match coefficients. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.

Find the general solution of \( \displaystyle y'' - 5y' + 6y = - 2 e^{- 2 x} \) by the method of undetermined coefficients.

Problem 6.241hard✓ Every equation proved

Find the general solution of \( \displaystyle y'' + 3y' + 2y = 2 \cos{\left(2 x \right)} \) by the method of undetermined coefficients.

Problem 6.242hard✓ Nihil obstat

Find the general solution of \( \displaystyle y'' - 5y' + 6y = - 4 \sin{\left(2 x \right)} \) by the method of undetermined coefficients.

Problem 6.243hard✓ Every equation proved

Solve \( \displaystyle y'' + 3y' - 4y = - \sin{\left(2 x \right)} \) with \( \displaystyle y(0) = 2 \), \( \displaystyle y'(0) = -1 \).

Problem 6.244hard✓ Nihil obstat

Find the general solution of \( \displaystyle y'' + y' - 12y = 5 e^{4 x} \) by the method of undetermined coefficients.

Problem 6.245hard✓ Nihil obstat

Find the general solution of \( \displaystyle y'' + 4y' + 3y = 3 x - 1 \) by the method of undetermined coefficients.

Problem 6.246hard✓ Nihil obstat

Find the general solution of \( \displaystyle y'' + 5y' + 4y = e^{4 x} \) by the method of undetermined coefficients.

Problem 6.247hard✓ Every equation proved

Find the general solution of \( \displaystyle y'' + 3y' + 2y = 5 x + 6 \) by the method of undetermined coefficients.

Problem 6.248hard✓ Every equation proved

Solve \( \displaystyle y'' - 5y' + 6y = 12 \) with \( \displaystyle y(0) = 2 \), \( \displaystyle y'(0) = -2 \).

Problem 6.249hard✓ Every equation proved

Find the general solution of \( \displaystyle y'' + 7y' + 12y = 4 x - 6 \) by the method of undetermined coefficients.

Problem 6.250hard✓ Nihil obstat