60.2.273 problem 849

Internal problem ID [10860]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 849
Date solved : Tuesday, January 28, 2025 at 05:25:54 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=-\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \end{align*}

✓ Solution by Maple

Time used: 0.278 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.708 (sec). Leaf size: 73

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

\[ y(x)\to \frac {x^8}{16}+\frac {x^7}{6}+\frac {x^6}{9}+\frac {x^5}{2}-\frac {1}{6} (-4+3 c_1) x^4-\frac {2 c_1 x^3}{3}+\frac {3 x^2}{4}+x-2 c_1 x+c_1{}^2 \]