75.12.39 problem 313

Internal problem ID [16905]
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
Date solved : Tuesday, January 28, 2025 at 09:40:30 AM
CAS classification : [_rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.104 (sec). Leaf size: 59

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

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

✓ Solution by Mathematica

Time used: 0.856 (sec). Leaf size: 46

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

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