60.2.271 problem 847

Internal problem ID [10858]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 847
Date solved : Tuesday, January 28, 2025 at 05:25:12 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.308 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.751 (sec). Leaf size: 69

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

\[ y(x)\to \frac {1}{144} \left (-9 x^8-24 x^7-16 x^6-72 x^5+24 (-4+3 c_1) x^4+96 c_1 x^3-108 x^2+72 (1+4 c_1) x+36-144 c_1{}^2\right ) \]