Internal problem ID [3483]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 750.
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: 0.157 (sec). Leaf size: 21
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: 60.112 (sec). Leaf size: 87
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*}