60.2.77 problem 653

Internal problem ID [10664]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 653
Date solved : Monday, January 27, 2025 at 09:23:10 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.173 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.536 (sec). Leaf size: 31

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

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