Internal problem ID [3608]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 880.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, _dAlembert]
Solve \begin {gather*} \boxed {2 x \left (y^{\prime }\right )^{2}+\left (2 x -y\right ) y^{\prime }+1-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 146
dsolve(2*x*diff(y(x),x)^2+(2*x-y(x))*diff(y(x),x)+1-y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\left (-2 \left ({\mathrm e}^{\RootOf \left (-x \,{\mathrm e}^{3 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +1\right )}-1\right )^{2}-2 \,{\mathrm e}^{\RootOf \left (-x \,{\mathrm e}^{3 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +1\right )}+2\right ) {\mathrm e}^{-\RootOf \left (-x \,{\mathrm e}^{3 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +1\right )} x +{\mathrm e}^{-\RootOf \left (-x \,{\mathrm e}^{3 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +1\right )} \]
✓ Solution by Mathematica
Time used: 1.414 (sec). Leaf size: 49
DSolve[2 x (y'[x])^2+(2 x-y[x])y'[x]+1-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\frac {\frac {1}{K[1]+1}+\log (K[1]+1)}{K[1]^2}+\frac {c_1}{K[1]^2},y(x)=2 x K[1]+\frac {1}{K[1]+1}\right \},\{y(x),K[1]\}\right ] \]