60.2.78 problem 654

Internal problem ID [10665]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 654
Date solved : Monday, January 27, 2025 at 09:23:14 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=-\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (1+x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.204 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.435 (sec). Leaf size: 37

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

\[ y(x)\to \frac {1}{12} \left (-4 x^2+9 \log ^2(x+1)-18 c_1 \log (x+1)+9 c_1{}^2\right ) \]