Laplace integral method for a differential equation
= Laplace integral method for a differential equation
{c}
Laplace's integral method seeks $y(z)=\int_Ce^{zt}f(t)\,dt$. Substitution into the differential equation and integration by parts transfer multiplication by $z$ into differentiation with respect to $t$, producing a first-order equation for $f$ and endpoint conditions for $C$.