29.30.20 problem 880

Internal problem ID [5460]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 880
Date solved : Tuesday, March 04, 2025 at 09:40:05 PM
CAS classification : [_rational, _dAlembert]

\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 110

ode:=2*x*diff(y(x),x)^2+(2*x-y(x))*diff(y(x),x)+1-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = -2 \left (x \,{\mathrm e}^{\operatorname {RootOf}\left (-x \,{\mathrm e}^{3 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +1\right )}-{\mathrm e}^{2 \operatorname {RootOf}\left (-x \,{\mathrm e}^{3 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +1\right )} x -\frac {1}{2}\right ) {\mathrm e}^{-\operatorname {RootOf}\left (-x \,{\mathrm e}^{3 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +1\right )} \]

✓ Mathematica. Time used: 1.408 (sec). Leaf size: 53

ode=2 x (D[y[x],x])^2+(2 x-y[x])D[y[x],x]+1-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=\frac {\log (K[1]+1)-\frac {K[1]}{K[1]+1}}{K[1]^2}+\frac {c_1}{K[1]^2},y(x)=2 x K[1]+\frac {1}{K[1]+1}\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x)**2 + (2*x - y(x))*Derivative(y(x), x) - y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out