60.2.364 problem 941

Internal problem ID [10951]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 941
Date solved : Monday, January 27, 2025 at 10:30:31 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}-192 x y^{2}+12 y x^{4}-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 35

dsolve(diff(y(x),x) = (-32*x*y(x)-72*x^3+32*x^2-32*x+64*y(x)^3+48*x^2*y(x)^2-192*x*y(x)^2+12*y(x)*x^4-96*x^3*y(x)+192*x^2*y(x)+x^6-12*x^5+48*x^4)/(64*y(x)+16*x^2-64*x+64),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 72

DSolve[D[y[x],x] == (-32*x + 32*x^2 - 72*x^3 + 48*x^4 - 12*x^5 + x^6 - 32*x*y[x] + 192*x^2*y[x] - 96*x^3*y[x] + 12*x^4*y[x] - 192*x*y[x]^2 + 48*x^2*y[x]^2 + 64*y[x]^3)/(64 - 64*x + 16*x^2 + 64*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {-2 x^2+8 x-8 y(x)+4}{\sqrt [3]{11} \left ((x-2)^2+4 y(x)\right )}}\frac {1}{K[1]^3+\frac {15 K[1]}{11^{2/3}}+1}dK[1]=\frac {1}{9} 11^{2/3} x+c_1,y(x)\right ] \]