60.2.366 problem 943

Internal problem ID [10953]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 943
Date solved : Monday, January 27, 2025 at 10:30:44 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 x^{2} y^{2}-384 x y^{2}+24 y x^{4}-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \end{align*}

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 41

dsolve(diff(y(x),x) = (-128*x*y(x)-24*x^3+32*x^2-128*x+512*y(x)^3+192*x^2*y(x)^2-384*x*y(x)^2+24*y(x)*x^4-96*x^3*y(x)+96*x^2*y(x)+x^6-6*x^5+12*x^4)/(512*y(x)+64*x^2-128*x+512),y(x), singsol=all)
 

\[ y = -\frac {x^{2}}{8}+\frac {x}{4}+\operatorname {RootOf}\left (-x +4 \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a} +1}{4 \textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a} \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.245 (sec). Leaf size: 75

DSolve[D[y[x],x] == (-128*x + 32*x^2 - 24*x^3 + 12*x^4 - 6*x^5 + x^6 - 128*x*y[x] + 96*x^2*y[x] - 96*x^3*y[x] + 24*x^4*y[x] - 384*x*y[x]^2 + 192*x^2*y[x]^2 + 512*y[x]^3)/(512 - 128*x + 64*x^2 + 512*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [362^{2/3} x+144 c_1=144 \int _1^{\frac {-11 x^2+22 x-88 y(x)+8}{\sqrt [3]{362} \left (x^2-2 x+8 y(x)+8\right )}}\frac {1}{K[1]^3+\frac {69 K[1]}{362^{2/3}}+1}dK[1],y(x)\right ] \]