57.1.50 problem 50

Internal problem ID [9034]
Book : First order enumerated odes
Section : section 1
Problem number : 50
Date solved : Monday, January 27, 2025 at 05:27:42 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 15.456 (sec). Leaf size: 100

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 1-x \\ \end{align*}