4.16.4 \(y'(x)^2=x-y(x)\)

ODE
\[ y'(x)^2=x-y(x) \] ODE Classification

[[_homogeneous, `class C`], _dAlembert]

Book solution method
No Missing Variables ODE, Solve for \(x\)

Mathematica
cpu = 0.20376 (sec), leaf count = 46

\[\left \{\left \{y(x)\to -W\left (-e^{\frac {1}{2} \left (c_1-x-2\right )}\right ){}^2-2 W\left (-e^{\frac {1}{2} \left (c_1-x-2\right )}\right )+x-1\right \}\right \}\]

Maple
cpu = 0.014 (sec), leaf count = 35

\[ \left \{ [x \left ({\it \_T} \right ) =-2\,{\it \_T}-2\,\ln \left ({\it \_T}-1 \right ) +{\it \_C1},y \left ({\it \_T} \right ) =-{{\it \_T}}^{2}-2\,{\it \_T}-2\,\ln \left ({\it \_T}-1 \right ) +{\it \_C1}] \right \} \] Mathematica raw input

DSolve[y'[x]^2 == x - y[x],y[x],x]

Mathematica raw output

{{y[x] -> -1 + x - 2*ProductLog[-E^((-2 - x + C[1])/2)] - ProductLog[-E^((-2 - x
 + C[1])/2)]^2}}

Maple raw input

dsolve(diff(y(x),x)^2 = x-y(x), y(x),'implicit')

Maple raw output

[x(_T) = -2*_T-2*ln(_T-1)+_C1, y(_T) = -_T^2-2*_T-2*ln(_T-1)+_C1]