Internal problem ID [9173]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 838.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {y^{\prime }-\frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 y x^{3}-100 \sqrt {x}\, y+4 x^{6}+40 x^{\frac {7}{2}}+100 x}{25 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x) = 1/25*(30*x^3+25*x^(1/2)+25*y(x)^2-20*x^3*y(x)-100*y(x)*x^(1/2)+4*x^6+40*x^(7/2)+100*x)/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (10 c_{1} -10 \ln \left (x \right )\right ) \sqrt {x}+2 c_{1} x^{3}-2 x^{3} \ln \left (x \right )+5}{-5 \ln \left (x \right )+5 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.304 (sec). Leaf size: 48
DSolve[y'[x] == (Sqrt[x] + 4*x + (6*x^3)/5 + (8*x^(7/2))/5 + (4*x^6)/25 - 4*Sqrt[x]*y[x] - (4*x^3*y[x])/5 + y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\frac {1}{-\log (x)+c_1} \\ y(x)\to \frac {2}{5} \left (x^3+5 \sqrt {x}\right ) \\ \end{align*}