60.2.98 problem 674

Internal problem ID [10685]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 674
Date solved : Monday, January 27, 2025 at 09:26:16 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.216 (sec). Leaf size: 27

dsolve(diff(y(x),x) = -1/2*(x^2-x-2-2*(x^2-4*x+4*y(x))^(1/2))/(x+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.648 (sec). Leaf size: 32

DSolve[D[y[x],x] == (1 + x/2 - x^2/2 + Sqrt[-4*x + x^2 + 4*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^2}{4}+x+\log ^2(x+1)-2 c_1 \log (x+1)+c_1{}^2 \]