Internal problem ID [8172]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 592.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x) = 1/5*(6*x^3+5*x^(1/2)+5*F(y(x)-2/5*x^3-2*x^(1/2)))/x,y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {1}{F \left (\textit {\_a} -\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}d \textit {\_a} -\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.341 (sec). Leaf size: 241
DSolve[y'[x] == (Sqrt[x] + (6*x^3)/5 + F[-2*Sqrt[x] - (2*x^3)/5 + y[x]])/x,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}-\frac {F\left (-\frac {2 x^3}{5}-2 \sqrt {x}+K[2]\right ) \int _1^x\left (-\frac {6 F'\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right ) K[1]^2}{5 F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )^2}-\frac {F'\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )}{F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )^2 \sqrt {K[1]}}\right )dK[1]+1}{F\left (-\frac {2 x^3}{5}-2 \sqrt {x}+K[2]\right )}dK[2]+\int _1^x\left (\frac {6 K[1]^2}{5 F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+y(x)\right )}+\frac {1}{F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+y(x)\right ) \sqrt {K[1]}}+\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ] \]