Internal problem ID [3579]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 848.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+2 y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 63
dsolve(x*diff(y(x),x)^2+2*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{2 \RootOf \left (-x \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} x -2 \,{\mathrm e}^{\textit {\_Z}}+c_{1}+2 \textit {\_Z} -x \right )}+2 \,{\mathrm e}^{\RootOf \left (-x \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} x -2 \,{\mathrm e}^{\textit {\_Z}}+c_{1}+2 \textit {\_Z} -x \right )} \]
✓ Solution by Mathematica
Time used: 13.19 (sec). Leaf size: 50
DSolve[x (y'[x])^2+2 y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\frac {2 \log (K[1])-2 K[1]}{(K[1]-1)^2}+\frac {c_1}{(K[1]-1)^2},y(x)=x K[1]^2+2 K[1]\right \},\{y(x),K[1]\}\right ] \]