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 = 0.294967 (sec), leaf count = 46
\[\left \{\left \{y(x)\to -W\left (-e^{\frac {1}{2} (-x-2+c_1)}\right ){}^2-2 W\left (-e^{\frac {1}{2} (-x-2+c_1)}\right )+x-1\right \}\right \}\]
Maple ✓
cpu = 0.107 (sec), leaf count = 21
\[\left [y \left (x \right ) = -\left (\LambertW \left (\textit {\_C1} \,{\mathrm e}^{-\frac {x}{2}-1}\right )+1\right )^{2}+x\right ]\] 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))
Maple raw output
[y(x) = -(LambertW(_C1*exp(-1/2*x-1))+1)^2+x]