60.2.362 problem 939

Internal problem ID [10949]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 939
Date solved : Monday, January 27, 2025 at 10:30:23 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class C`]]

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

✓ Solution by Maple

Time used: 0.129 (sec). Leaf size: 79

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

\[ x +\frac {2 \ln \left (2\right )}{5}+\frac {2 \ln \left (16 y^{2}+\left (-8 x^{2}-16 x +16\right ) y+x^{4}+4 x^{3}-8 x +8\right )}{5}-\frac {2 \arctan \left (-2 y+\frac {x^{2}}{2}+x -1\right )}{5}-\frac {4 \ln \left (4 y-x^{2}-2 x -4\right )}{5}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.319 (sec). Leaf size: 86

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

\[ \text {Solve}\left [(-74)^{2/3} x+36 c_1=36 \int _1^{-\frac {(-1)^{2/3} \left (5 x^2+10 x-20 y(x)+4\right )}{\sqrt [3]{74} \left (x^2+2 x-4 y(x)-4\right )}}\frac {1}{K[1]^3-\frac {33 \sqrt [3]{-1} K[1]}{74^{2/3}}+1}dK[1],y(x)\right ] \]