(a) Show that the change of variables y = x − 1 + w transforms the Riccati differential equation y ′ + 7 x − 1 y − 3 y 2 = 3 x − 2 ( 1.8.24 ) into the Bernoulli equation w ′ + x − 1 w = 3 w 2 . ( 1.8.25 ) (b) Solve Equation (1.8.25), and hence determine the general solution to (1.8.24).
(a) Show that the change of variables y = x − 1 + w transforms the Riccati differential equation y ′ + 7 x − 1 y − 3 y 2 = 3 x − 2 ( 1.8.24 ) into the Bernoulli equation w ′ + x − 1 w = 3 w 2 . ( 1.8.25 ) (b) Solve Equation (1.8.25), and hence determine the general solution to (1.8.24).
Solution Summary: The author proves that the change of variables y=x-1+w transforms the Riccati differential equation into Bernoulli equation.
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