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...Computable integrability chapter riccati equation e kartashova a shabat contents introduction general solution of re x transformation group singularities solutions dierential equations related to linear second order schwarzian modied asymptotic rewith parameter soliton like potentials finite gap summary exercises for b c is one the most simple nonlinear because it rst and with quadratic nonlinearity obviously this was reason that as soon newton invented be investigated extensively since end th century in considered ode w u polynomial function evidently cases degu corre spond airy hermite transcendent functions respectively below we show integrable quadratures only f though corresponding self at glance simpler thus new transcendents were introduced odewith i res some classes are known have instance y ay bx where all constant respect d bernoulli discovered elementary if or k results about pre sented which make widely usable numerous applications dierent branches physics mathematics how s...