ODE
\[ y''(x)=(a-x) y'(x)^3 \] ODE Classification
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0390364 (sec), leaf count = 61
\[\left \{\left \{y(x)\to c_2-\log \left (\sqrt {-2 a x-2 c_1+x^2}-a+x\right )\right \},\left \{y(x)\to \log \left (\sqrt {-2 a x-2 c_1+x^2}-a+x\right )+c_2\right \}\right \}\]
Maple ✓
cpu = 0.111 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) =-\ln \left ( x-a+\sqrt {{a}^{2}-2\,ax+{x}^{2}-{\it \_C1}} \right ) +{\it \_C2},y \left ( x \right ) =\ln \left ( x-a+\sqrt {{a}^{2}-2\,ax+{x}^{2}-{\it \_C1}} \right ) +{\it \_C2} \right \} \] Mathematica raw input
DSolve[y''[x] == (a - x)*y'[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> C[2] - Log[-a + x + Sqrt[-2*a*x + x^2 - 2*C[1]]]}, {y[x] -> C[2] + Log[-a + x + Sqrt[-2*a*x + x^2 - 2*C[1]]]}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = (a-x)*diff(y(x),x)^3, y(x),'implicit')
Maple raw output
y(x) = ln(x-a+(a^2-2*a*x+x^2-_C1)^(1/2))+_C2, y(x) = -ln(x-a+(a^2-2*a*x+x^2-_C1)^(1/2))+_C2