60.2.145 problem 721

Internal problem ID [10732]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 721
Date solved : Monday, January 27, 2025 at 09:36:28 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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)
 

\[ y = \frac {x^{3}}{6}-\frac {3}{2 x^{{3}/{2}}-3 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.205 (sec). Leaf size: 38

DSolve[D[y[x],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*}