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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.1 The Geometric Series, #36 · Calculus · Series

The differential equation … starts from

The differential equation $d y / d x = y^{2}$ starts from $y (0) = b$ .
From the equation and its derivatives find $y^{'}$ , $y^{''}$ , $y^{'''}$ at $x = 0$ ,
and construct the start of a series that matches those derivatives. Can
you recognize $y (x)$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.1 The Geometric Series, #36

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