Internal problem ID [8164]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 584.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.098 (sec). Leaf size: 35
dsolve(diff(y(x),x) = 2*a/(y(x)+2*F(y(x)^2-4*a*x)*a),y(x), singsol=all)
\[ \frac {y \relax (x )}{2 a}+\frac {\int _{}^{y \relax (x )^{2}-4 a x}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a}}{8 a^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 115
DSolve[y'[x] == (2*a)/(2*a*F[-4*a*x + y[x]^2] + y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{4 a^2 F\left (K[2]^2-4 a x\right )}-\frac {2 a \int _1^x\frac {K[2] F'\left (K[2]^2-4 a K[1]\right )}{a F\left (K[2]^2-4 a K[1]\right )^2}dK[1]-1}{2 a}\right )dK[2]+\int _1^x-\frac {1}{2 a F\left (y(x)^2-4 a K[1]\right )}dK[1]=c_1,y(x)\right ] \]