Internal problem ID [6613]
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]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 24
dsolve(diff(y(x),x)^2=x+y(x),y(x), singsol=all)
\[ y \relax (x ) = \left (-\LambertW \left (-c_{1} {\mathrm e}^{-\frac {x}{2}-1}\right )-1\right )^{2}-x \]
✓ Solution by Mathematica
Time used: 60.183 (sec). Leaf size: 89
DSolve[(y'[x])^2==x+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ProductLog}\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right ) \left (2+\text {ProductLog}\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right )\right )-x+1 \\ y(x)\to \text {ProductLog}\left (e^{\frac {1}{2} (-x-2+c_1)}\right ) \left (2+\text {ProductLog}\left (e^{\frac {1}{2} (-x-2+c_1)}\right )\right )-x+1 \\ \end{align*}