60.2.139 problem 715

Internal problem ID [10726]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 715
Date solved : Tuesday, January 28, 2025 at 05:08:47 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2+2 x} \end{align*}

✓ Solution by Maple

Time used: 0.299 (sec). Leaf size: 39

dsolve(diff(y(x),x) = 1/2*(-x^2+x+2+2*x^3*(x^2-4*x+4*y(x))^(1/2))/(x+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.371 (sec). Leaf size: 50

DSolve[D[y[x],x] == (1 + x/2 - x^2/2 + x^3*Sqrt[-4*x + x^2 + 4*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
 

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