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Differential Equationshard
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Consider the Riccati equation y′=Q(x)y2+P(x)y+R(x)y' = Q(x)y^2 + P(x)y + R(x)y′=Q(x)y2+P(x)y+R(x). Given a particular solution y1(x)y_1(x)y1​(x), what is the transformation y=y1(x)+u(x)y = y_1(x) + u(x)y=y1​(x)+u(x) that reduces this to a Bernoulli equation?