29.25 problem 847

Internal problem ID [3578]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 29
Problem number: 847.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_rational, _dAlembert]

Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+y^{\prime }-y=0} \end {gather*}

Solution by Maple

Time used: 0.078 (sec). Leaf size: 57

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

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

Solution by Mathematica

Time used: 0.916 (sec). Leaf size: 46

DSolve[x (y'[x])^2+y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
 

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