Internal problem ID [15175]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 313.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, _dAlembert]
\[ \boxed {y^{\prime }+x {y^{\prime }}^{2}-y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 59
dsolve(diff(y(x),x)+x*diff(y(x),x)^2-y(x)=0,y(x), singsol=all)
\[ y = 2 \,{\mathrm e}^{\operatorname {RootOf}\left (-x \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} x +\textit {\_Z} +c_{1} -x -{\mathrm e}^{\textit {\_Z}}\right )} x +\operatorname {RootOf}\left (-x \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} x +\textit {\_Z} +c_{1} -x -{\mathrm e}^{\textit {\_Z}}\right )+c_{1} -x \]
✓ Solution by Mathematica
Time used: 0.881 (sec). Leaf size: 46
DSolve[y'[x]+x*y'[x]^2-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\frac {\log (K[1])-K[1]}{(K[1]-1)^2}+\frac {c_1}{(K[1]-1)^2},y(x)=x K[1]^2+K[1]\right \},\{y(x),K[1]\}\right ] \]