60.2.67 problem 643

Internal problem ID [10654]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 643
Date solved : Monday, January 27, 2025 at 09:21:57 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.153 (sec). Leaf size: 22

dsolve(diff(y(x),x) = 1/3*x*(-2+3*x*(x^2+3*y(x))^(1/2)),y(x), singsol=all)
 

\[ c_{1} +\frac {x^{3}}{2}-\sqrt {x^{2}+3 y} = 0 \]

✓ Solution by Mathematica

Time used: 0.288 (sec). Leaf size: 31

DSolve[D[y[x],x] == (x*(-2 + 3*x*Sqrt[x^2 + 3*y[x]]))/3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} \left (x^6-6 c_1 x^3-4 x^2+9 c_1{}^2\right ) \]