29.29.25 problem 847

Internal problem ID [5430]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 847
Date solved : Monday, January 27, 2025 at 11:23:23 AM
CAS classification : [_rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 59

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

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

✓ Solution by Mathematica

Time used: 0.862 (sec). Leaf size: 46

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

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