Internal problem ID [8824]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 489.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational]
\[ \boxed {y^{2} {y^{\prime }}^{2}+2 x y^{\prime } y+a y^{2}=-x b -c} \]
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 365
dsolve(y(x)^2*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+a*y(x)^2+b*x+c = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {2 \sqrt {a \left (a \left (a x -\frac {1}{2} b +x \right )^{2} \left (a +1\right )^{2} \operatorname {RootOf}\left (-2 b \ln \left (2 a x -b +2 x \right )+b \left (\int _{}^{\textit {\_Z}}-\frac {4 \textit {\_a} \,a^{2}-\sqrt {-\left (4 \textit {\_a} \,a^{3}+8 \textit {\_a} \,a^{2}+4 \textit {\_a} a -1\right ) {\mathrm e}^{\frac {4 a}{b}} {\mathrm e}^{\frac {4}{b}}}\, {\mathrm e}^{-\frac {2 \left (a +1\right )}{b}}+8 \textit {\_a} a +4 \textit {\_a} +1}{\textit {\_a} \left (4 \textit {\_a} \,a^{2}+8 \textit {\_a} a +4 \textit {\_a} +a +2\right )}d \textit {\_a} \right )+4 c_{1} a +4 c_{1} \right )+\frac {\left (-b x -c \right ) a^{2}}{4}+\frac {\left (-\frac {b x}{2}-c \right ) a}{2}-\frac {b^{2}}{16}-\frac {c}{4}\right )}}{a \left (a +1\right )} \\ y \left (x \right ) &= \frac {2 \sqrt {a \left (a \left (a x -\frac {1}{2} b +x \right )^{2} \left (a +1\right )^{2} \operatorname {RootOf}\left (-2 b \ln \left (2 a x -b +2 x \right )+b \left (\int _{}^{\textit {\_Z}}-\frac {4 \textit {\_a} \,a^{2}-\sqrt {-\left (4 \textit {\_a} \,a^{3}+8 \textit {\_a} \,a^{2}+4 \textit {\_a} a -1\right ) {\mathrm e}^{\frac {4 a}{b}} {\mathrm e}^{\frac {4}{b}}}\, {\mathrm e}^{-\frac {2 \left (a +1\right )}{b}}+8 \textit {\_a} a +4 \textit {\_a} +1}{\textit {\_a} \left (4 \textit {\_a} \,a^{2}+8 \textit {\_a} a +4 \textit {\_a} +a +2\right )}d \textit {\_a} \right )+4 c_{1} a +4 c_{1} \right )+\frac {\left (-b x -c \right ) a^{2}}{4}+\frac {\left (-\frac {b x}{2}-c \right ) a}{2}-\frac {b^{2}}{16}-\frac {c}{4}\right )}}{a \left (a +1\right )} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[c + b*x + a*y[x]^2 + 2*x*y[x]*y'[x] + y[x]^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Timed out