Second-Order Homogeneous ODEs: Real Characteristic Roots (Differential Equations)
Free printable university Differential Equations worksheet on second-order linear homogeneous ODEs with constant coefficients: distinct and repeated real characteristic roots, plus initial value problems.
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Differential Equations · Math worksheet
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Second-Order Homogeneous ODEs: Real Characteristic Roots
Solve each equation with the characteristic equation r² + pr + q = 0. Give the general solution, or apply the initial conditions where they are provided. Watch for repeated roots.
- 1.y″ + 2y′ - 8y = 0
- 2.y″ + y′ - 12y = 0
- 3.y″ - 5y′ + 6y = 0
- 4.y″ - y′ - 6y = 0
- 5.y″ - 2y′ = 0
- 6.y″ - 2y′ - 3y = 0
- 7.y″ + 8y′ + 16y = 0
- 8.y″ + 6y′ + 9y = 0
- 9.y″ - 4y′ + 4y = 0
- 10.y″ - 7y′ + 12y = 0, y(0) = 0, y′(0) = 2
- 11.y″ - 4y′ + 3y = 0, y(0) = 0, y′(0) = -4
- 12.y″ - 2y′ = 0, y(0) = 3, y′(0) = 2
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