60.2.141 problem 717

Internal problem ID [10728]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 717
Date solved : Monday, January 27, 2025 at 09:35:36 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=-\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (1+x \right )} \end{align*}

Solution by Maple

Time used: 0.265 (sec). Leaf size: 33

dsolve(diff(y(x),x) = -1/2*(x^2+x+a*x+a-2*(x^2+2*a*x+a^2+4*y(x))^(1/2))/(x+1),y(x), singsol=all)
 
\[ c_{1} +\frac {a}{2}+2 \ln \left (x +1\right )-\sqrt {a^{2}+2 a x +x^{2}+4 y} = 0 \]

Solution by Mathematica

Time used: 0.766 (sec). Leaf size: 44

DSolve[D[y[x],x] == (-1/2*a - x/2 - (a*x)/2 - x^2/2 + Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to -\frac {a^2}{4}-\frac {a x}{2}-\frac {x^2}{4}+\log ^2(x+1)-2 c_1 \log (x+1)+c_1{}^2 \]