Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.7 Hyperbolic Functions, #56 · Calculus · Differentiation rules

The simplest nonlinear wave equation (Burgers' equation) yields a waveform … that…

The simplest nonlinear wave equation (Burgers' equation) yields a waveform $W (x)$ that satisfies $W^{''} = W W^{'} - W^{'}$ . One integration gives $W^{'} = \frac{1}{2} W^{2} - W$ .
(a) Separate variables and integrate:
$d x = d W / (\frac{1}{2} W^{2} - W) = - d W / (2 - W) - d W / W$ .
(b) Check $W^{'} = \frac{1}{2} W^{2} - W$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.7 Hyperbolic Functions, #56

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