Internal problem ID [9056]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 721.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime }-\frac {\left (18 x^{\frac {3}{2}}+36 y^{2}-12 y x^{3}+x^{6}\right ) \sqrt {x}}{36}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x) = 1/36*(18*x^(3/2)+36*y(x)^2-12*x^3*y(x)+x^6)*x^(1/2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{3}}{6}+\frac {1}{c_{1} -\frac {2 x^{\frac {3}{2}}}{3}} \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 38
DSolve[y'[x] == (Sqrt[x]*(18*x^(3/2) + x^6 - 12*x^3*y[x] + 36*y[x]^2))/36,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3}{6}+\frac {1}{-\frac {2 x^{3/2}}{3}+c_1} y(x)\to \frac {x^3}{6} \end{align*}