Internal problem ID [3581]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 850.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+4 y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 64
dsolve(x*diff(y(x),x)^2+4*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x \,{\mathrm e}^{2 \RootOf \left (-x \,{\mathrm e}^{2 \textit {\_Z}}+4 \,{\mathrm e}^{\textit {\_Z}} x -4 \,{\mathrm e}^{\textit {\_Z}}+c_{1}+8 \textit {\_Z} -4 x \right )}}{2}+2 \,{\mathrm e}^{\RootOf \left (-x \,{\mathrm e}^{2 \textit {\_Z}}+4 \,{\mathrm e}^{\textit {\_Z}} x -4 \,{\mathrm e}^{\textit {\_Z}}+c_{1}+8 \textit {\_Z} -4 x \right )} \]
✓ Solution by Mathematica
Time used: 30.717 (sec). Leaf size: 90
DSolve[x (y'[x])^2+4 y'[x]-2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=-\frac {2 (2 K[1]-y(K[1]))}{K[1]^2},y(x)=4 \left (\frac {2}{K[1]}+\log (K[1])\right ) \exp \left (-4 \left (\frac {1}{2} \log (2-K[1])-\frac {1}{2} \log (K[1])\right )\right )+c_1 \exp \left (-4 \left (\frac {1}{2} \log (2-K[1])-\frac {1}{2} \log (K[1])\right )\right )\right \},\{y(x),K[1]\}\right ] \]