Internal problem ID [3991]
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]
\[ \boxed {{y^{\prime }}^{2}+y=x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve(diff(y(x),x)^2 = x-y(x),y(x), singsol=all)
\[ y \left (x \right ) = -{\left (\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-\frac {x}{2}-1}\right )+1\right )}^{2}+x \]
✓ Solution by Mathematica
Time used: 27.515 (sec). Leaf size: 98
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 x-1 \end{align*}