60.2.281 problem 857

Internal problem ID [10868]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 857
Date solved : Tuesday, January 28, 2025 at 05:26:51 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \end{align*}

✓ Solution by Maple

Time used: 0.271 (sec). Leaf size: 32

dsolve(diff(y(x),x) = -1/4*x+1/4+(x^2-2*x+1+8*y(x))^(1/2)+x^2*(x^2-2*x+1+8*y(x))^(1/2)+x^3*(x^2-2*x+1+8*y(x))^(1/2),y(x), singsol=all)
 

\[ c_{1} +x^{4}+\frac {4 x^{3}}{3}+4 x -\sqrt {x^{2}+8 y-2 x +1} = 0 \]

✓ Solution by Mathematica

Time used: 0.821 (sec). Leaf size: 77

DSolve[D[y[x],x] == 1/4 - x/4 + Sqrt[1 - 2*x + x^2 + 8*y[x]] + x^2*Sqrt[1 - 2*x + x^2 + 8*y[x]] + x^3*Sqrt[1 - 2*x + x^2 + 8*y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^8}{8}+\frac {x^7}{3}+\frac {2 x^6}{9}+x^5+\left (\frac {4}{3}-c_1\right ) x^4-\frac {4 c_1 x^3}{3}+\frac {15 x^2}{8}+\left (\frac {1}{4}-4 c_1\right ) x-\frac {1}{8}+2 c_1{}^2 \]