Internal problem ID [8746]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 410.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, _dAlembert]
\[ \boxed {x {y^{\prime }}^{2}+4 y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 67
dsolve(x*diff(y(x),x)^2+4*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = 2 x \,{\mathrm e}^{\operatorname {RootOf}\left (-x \,{\mathrm e}^{2 \textit {\_Z}}+4 x \,{\mathrm e}^{\textit {\_Z}}-4 \,{\mathrm e}^{\textit {\_Z}}+c_{1} +8 \textit {\_Z} -4 x \right )}+4 \operatorname {RootOf}\left (-x \,{\mathrm e}^{2 \textit {\_Z}}+4 x \,{\mathrm e}^{\textit {\_Z}}-4 \,{\mathrm e}^{\textit {\_Z}}+c_{1} +8 \textit {\_Z} -4 x \right )+\frac {c_{1}}{2}-2 x \]
✓ Solution by Mathematica
Time used: 30.799 (sec). Leaf size: 90
DSolve[-2*y[x] + 4*y'[x] + x*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=-\frac {2 (2 K[1]-y(K[1]))}{K[1]^2},y(x)=4 \left (\frac {2}{K[1]}+\log (K[1])\right ) \exp \left (-4 \left (\frac {1}{2} \log (2-K[1])-\frac {1}{2} \log (K[1])\right )\right )+c_1 \exp \left (-4 \left (\frac {1}{2} \log (2-K[1])-\frac {1}{2} \log (K[1])\right )\right )\right \},\{y(x),K[1]\}\right ] \]