60.2.233 problem 809

Internal problem ID [10820]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 809
Date solved : Monday, January 27, 2025 at 10:05:01 PM
CAS classification : [[_homogeneous, `class C`], _rational, _Abel]

\begin{align*} y^{\prime }&=\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 41

dsolve(diff(y(x),x) = (-125+300*x-240*x^2+64*x^3-80*y(x)^2+64*x*y(x)^2+64*y(x)^3)/(4*x-5)^3,y(x), singsol=all)
 

\[ y = -\frac {\operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} +\ln \left (4 x -5\right )+c_{1} \right ) \left (4 x -5\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.305 (sec). Leaf size: 109

DSolve[D[y[x],x] == (-125 + 300*x - 240*x^2 + 64*x^3 - 80*y[x]^2 + 64*x*y[x]^2 + 64*y[x]^3)/(-5 + 4*x)^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {\frac {192 y(x)}{(4 x-5)^3}+\frac {16}{(4 x-5)^2}}{16 \sqrt [3]{38} \sqrt [3]{\frac {1}{(4 x-5)^6}}}}\frac {1}{K[1]^3-\frac {6 \sqrt [3]{2} K[1]}{19^{2/3}}+1}dK[1]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(5-4 x)^6}\right )^{2/3} (5-4 x)^4 \log (5-4 x)+c_1,y(x)\right ] \]