60.2.88 problem 664

Internal problem ID [10675]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 664
Date solved : Monday, January 27, 2025 at 09:24:20 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.172 (sec). Leaf size: 25

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

\[ c_{1} +\frac {2 x^{3}}{3}-\sqrt {x^{2}+4 y-4 x} = 0 \]

✓ Solution by Mathematica

Time used: 0.438 (sec). Leaf size: 34

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

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