Mathematics · University
First-order exponential initial-value problem · formula reference
Use the initial condition after solving the homogeneous differential equation.
Formula
Use the initial condition after solving the homogeneous differential equation.
y(t) = y₀ exp(−kt)
Worked example
Solve y′ = −0.8y with y(0) = 63, then calculate y(8). Round the final result to 4 decimal places if needed.
Separation gives y = Ce^(−0.8t). Since C = 63, substitute t = 8.
0.1047
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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