Internal problem ID [8452]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 872.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-30 y x^{3}+12 x^{6}+70 x^{\frac {7}{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve(diff(y(x),x) = 1/5*(-30*x^3*y(x)+12*x^6+70*x^(7/2)-30*x^3-25*y(x)*x^(1/2)+50*x-25*x^(1/2)-25)/(-5*y(x)+2*x^3+10*x^(1/2)-5)/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {2 x^{3}}{5}+2 \sqrt {x}-\sqrt {c_{1}+2 \ln \relax (x )}-1 \\ y \relax (x ) = \frac {2 x^{3}}{5}+2 \sqrt {x}+\sqrt {c_{1}+2 \ln \relax (x )}-1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.447 (sec). Leaf size: 92
DSolve[y'[x] == (-5 - 5*Sqrt[x] + 10*x - 6*x^3 + 14*x^(7/2) + (12*x^6)/5 - 5*Sqrt[x]*y[x] - 6*x^3*y[x])/(x*(-5 + 10*Sqrt[x] + 2*x^3 - 5*y[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\sqrt {-\frac {1}{x}} \sqrt {-x (2 \log (x)+1+c_1)}-1 \\ y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\left (-\frac {1}{x}\right )^{3/2} x \sqrt {-x (2 \log (x)+1+c_1)}-1 \\ \end{align*}