Internal problem ID [8439]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 859.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {-x -f_{1}\left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.178 (sec). Leaf size: 63
dsolve(diff(y(x),x) = -(-x-_F1(y(x)^2-2*x))/(y(x)^2)^(1/2)/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {2 \RootOf \left (\ln \relax (x )-\left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1}\left (2 \textit {\_a} \right )}d \textit {\_a} \right )+2 c_{1}\right )+2 x} \\ y \relax (x ) = -\sqrt {2 \RootOf \left (\ln \relax (x )-\left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1}\left (2 \textit {\_a} \right )}d \textit {\_a} \right )+2 c_{1}\right )+2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.395 (sec). Leaf size: 101
DSolve[y'[x] == (x + F1[-2*x + y[x]^2])/(x*Sqrt[y[x]^2]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {K[2]^2}}{\text {F1}\left (K[2]^2-2 x\right )}-\int _1^x\frac {2 K[2] \text {F1}'\left (K[2]^2-2 K[1]\right )}{\text {F1}\left (K[2]^2-2 K[1]\right )^2}dK[1]\right )dK[2]+\int _1^x\left (-\frac {1}{K[1]}-\frac {1}{\text {F1}\left (y(x)^2-2 K[1]\right )}\right )dK[1]=c_1,y(x)\right ] \]