1--Copyright The Numerical Algorithms Group Limited 1994. 2-------------------------- nlode.input -------------------------------- 3)cl all 4-- this will be the unknown 5y := operator y 6 7-- some non-linear non-exact 1st order equations 8 9deq := (sin y x - x / y(x)) * differentiate(y x, x) = 1 10-- the result with no initial condition is a first integral 11-- when equated to any constant 12solve(deq, y, x) 13 14deq := differentiate(y x, x) = y(x) / (x + y(x) * log y x) 15solve(deq, y, x) 16-- same with initial condition y(1) = 1 17-- the result is a first integral if equated to 0 18solve(deq, y, x = 1, [1]) 19 20deq := (exp(- 2 * y x) - 2 * x * y x) * differentiate(y x, x) = y x 21solve(deq, y, x) 22 23-- this one has an independent parameter w, initial condition y(0) = 0 24deq := differentiate(y x, x) = w + y(x) / (1 - y x) 25solve(deq, y, x = 0, [0]) 26 27-- Bernoulli equation: the result is a first integral when equated to 28-- any constant, but it can be explicitly solved for y(x) 29deq := x^2 * differentiate(y x, x) + 2 * x * y x - y(x)^3 30solve(deq, y, x) 31 32-- Riccati equation: the result is a first integral when equated to 33-- any constant, but it can be explicitly solved for y(x) 34deq := differentiate(y x,x) = 1 + x^2 - 2 * x * y x + y(x)^2 35solve(deq, y, x) 36 37-- Riccati equation: the result is a first integral when equated to 38-- any constant, but it can be explicitly solved for y(x) 39deq := x^2 * differentiate(y x,x) = -1 - x * y x + x^2 * y(x)^2 40solve(deq, y, x) 41