First-Order Linear ODEs: The Integrating Factor (Differential Equations)
Free printable university Differential Equations worksheet on the integrating factor method for first-order linear ODEs y' + ay = g(x), with constant, exponential and polynomial forcing.
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Differential Equations · Math worksheet
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Math
First-Order Linear ODEs: The Integrating Factor
Solve each initial value problem with the integrating factor method: multiply through by μ = e^(∫a dx), recognise the left side as (μy)′, and integrate.
- 1.y′ - 3y = 9, y(0) = 2
- 2.y′ + 2y = -8x, y(0) = -1
- 3.y′ + 3y = 9x, y(0) = 1
- 4.y′ - 4y = 8, y(0) = -4
- 5.y′ + 2y = 8e^(2x), y(0) = -4
- 6.y′ - 2y = -4, y(0) = -3
- 7.y′ - 3y = -18x, y(0) = 3
- 8.y′ - 2y = 4x, y(0) = -4
- 9.y′ - 3y = , y(0) = 4
- 10.y′ + 2y = -6, y(0) = -4
- 11.y′ - y = -4e^(3x), y(0) = -3
- 12.y′ + 4y = 2e^(-3x), y(0) = 3
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