Internal problem ID [7366]
Book: First order enumerated odes
Section: section 1
Problem number: 50.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {{y^{\prime }}^{2}-y=x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x)^2=x+y(x),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-\frac {x}{2}-1}\right )^{2}+2 \operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-\frac {x}{2}-1}\right )-x +1 \]
✓ Solution by Mathematica
Time used: 18.817 (sec). Leaf size: 100
DSolve[(y'[x])^2==x+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to W\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right ){}^2+2 W\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right )-x+1 \\ 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 \\ y(x)\to 1-x \\ \end{align*}