60.2.86 problem 662

Internal problem ID [10673]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 662
Date solved : Monday, January 27, 2025 at 09:23:40 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.199 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.868 (sec). Leaf size: 37

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

\[ y(x)\to \frac {1}{36} \left (-4 x^6+24 c_1 x^3+9 x^2+18 x+9-36 c_1{}^2\right ) \]