Mathematics · University
A constant-forced first-order equation · formula reference
For y′ + ay = b with constant a > 0, b/a is the equilibrium value.
Formula
For y′ + ay = b with constant a > 0, b/a is the equilibrium value.
y(t)=b/a + (y₀−b/a)e^(−at)
Worked example
Given y′ + 6y = 10, y(0) = 16, calculate y(4). Round the final result to 4 decimal places if needed.
Use equilibrium 10/6, then add the decaying homogeneous term (16 − 10/6)e^(−6t).
1.6667
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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