60.2.123 problem 699

Internal problem ID [10710]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 699
Date solved : Tuesday, January 28, 2025 at 05:06:25 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.267 (sec). Leaf size: 36

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

\[ c_{1} +\frac {x^{3}}{2}-\frac {3 x^{2}}{4}-\frac {3 \ln \left (x +1\right )}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y} = 0 \]

✓ Solution by Mathematica

Time used: 0.882 (sec). Leaf size: 47

DSolve[D[y[x],x] == (x*(-2 - 2*x + 3*x^2*Sqrt[x^2 + 3*y[x]]))/(3*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \left (-x^2+\frac {1}{16} \left (2 x^3-3 x^2+6 x+6 \log \left (\frac {1}{x+1}\right )-6 c_1\right ){}^2\right ) \]