4.38.3 \(x y''(x)=(1-y(x)) y'(x)\)

ODE
\[ x y''(x)=(1-y(x)) y'(x) \] ODE Classification

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.26313 (sec), leaf count = 46

\[\left \{\left \{y(x)\to 2-\sqrt {2} \sqrt {2+c_1} \tanh \left (\frac {\sqrt {2+c_1} (-\log (x)+2 c_2)}{\sqrt {2}}\right )\right \}\right \}\]

Maple ✓
cpu = 0.47 (sec), leaf count = 24

\[\left [y \left (x \right ) = \frac {2 \textit {\_C1} +\tanh \left (\frac {\ln \left (x \right )-\textit {\_C2}}{2 \textit {\_C1}}\right )}{\textit {\_C1}}\right ]\] Mathematica raw input

DSolve[x*y''[x] == (1 - y[x])*y'[x],y[x],x]

Mathematica raw output

{{y[x] -> 2 - Sqrt[2]*Sqrt[2 + C[1]]*Tanh[(Sqrt[2 + C[1]]*(2*C[2] - Log[x]))/Sqr
t[2]]}}

Maple raw input

dsolve(x*diff(diff(y(x),x),x) = (1-y(x))*diff(y(x),x), y(x))

Maple raw output

[y(x) = (2*_C1+tanh(1/2*(ln(x)-_C2)/_C1))/_C1]