Undetermined Coefficients: An Introduction (Differential Equations)
Free printable university Differential Equations worksheet introducing the method of undetermined coefficients for non-homogeneous second-order ODEs with polynomial or exponential forcing terms.
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Differential Equations · Math worksheet
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Undetermined Coefficients: An Introduction
Find the general solution of each non-homogeneous equation: solve the characteristic equation for the complementary solution, then match a particular solution of the same form as the forcing term (constant, linear, or exponential).
- 1.y″ + 2y′ - 8y = 8
- 2.y″ - 4y = 4
- 3.y″ - 5y′ + 6y = -18
- 4.y″ + 3y′ - 4y = 8
- 5.y″ + 2y′ - 8y = 8x - 26
- 6.y″ + 5y′ + 4y = 4x + 1
- 7.y″ + 7y′ + 12y = 12x - 29
- 8.y″ + 5y′ + 6y = 12x + 4
- 9.y″ - 2y′ - 3y = 8e^(x)
- 10.y″ - y′ - 6y = -8e^(-x)
- 11.y″ + 3y′ - 4y = 6e^(-2x)
- 12.y″ + 5y′ + 4y = 18e^(2x)
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