60.2.224 problem 800

Internal problem ID [10811]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 800
Date solved : Monday, January 27, 2025 at 10:02:51 PM
CAS classification : [[_homogeneous, `class C`], _rational, _Abel]

\begin{align*} y^{\prime }&=\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 41

dsolve(diff(y(x),x) = (-b^3+6*b^2*x-12*b*x^2+8*x^3-4*y(x)^2*b+8*x*y(x)^2+8*y(x)^3)/(2*x-b)^3,y(x), singsol=all)
 

\[ y = \frac {\operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} +\ln \left (-2 x +b \right )+c_{1} \right ) \left (-2 x +b \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.404 (sec). Leaf size: 109

DSolve[D[y[x],x] == (-b^3 + 6*b^2*x - 12*b*x^2 + 8*x^3 - 4*b*y[x]^2 + 8*x*y[x]^2 + 8*y[x]^3)/(-b + 2*x)^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {\frac {4}{(b-2 x)^2}-\frac {24 y(x)}{(b-2 x)^3}}{4 \sqrt [3]{38} \sqrt [3]{\frac {1}{(b-2 x)^6}}}}\frac {1}{K[1]^3-\frac {6 \sqrt [3]{2} K[1]}{19^{2/3}}+1}dK[1]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(b-2 x)^6}\right )^{2/3} (b-2 x)^4 \log (b-2 x)+c_1,y(x)\right ] \]