29.26.14 problem 750

Internal problem ID [5335]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 750
Date solved : Monday, January 27, 2025 at 11:15:42 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} {y^{\prime }}^{2}&=x -y \end{align*}

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 31

dsolve(diff(y(x),x)^2 = x-y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-1-\frac {x}{2}}\right )^{2}-2 \operatorname {LambertW}\left (c_{1} {\mathrm e}^{-1-\frac {x}{2}}\right )+x -1 \]

✓ Solution by Mathematica

Time used: 15.360 (sec). Leaf size: 98

DSolve[(D[y[x],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*}