29.29.26 problem 848

Internal problem ID [5431]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 848
Date solved : Monday, January 27, 2025 at 11:23:24 AM
CAS classification : [_rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 65

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

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

✓ Solution by Mathematica

Time used: 11.336 (sec). Leaf size: 50

DSolve[x (D[y[x],x])^2+2 D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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