60.2.352 problem 929

Internal problem ID [10939]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 929
Date solved : Monday, January 27, 2025 at 10:25:59 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=-\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 x^{2} y^{2}+x^{3} y^{3}}{32 y x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 42

dsolve(diff(y(x),x) = -1/32/y(x)*(16*x*y(x)^3-8*y(x)^3-8*y(x)+8*x*y(x)^2-2*x^2*y(x)^3-8+12*x*y(x)-6*x^2*y(x)^2+x^3*y(x)^3)/x,y(x), singsol=all)
 

\[ y = \frac {18}{58 \operatorname {RootOf}\left (-324 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \left (x \right )+12 c_{1} \right )+9 x -6} \]

✓ Solution by Mathematica

Time used: 0.264 (sec). Leaf size: 74

DSolve[D[y[x],x] == (1/4 + y[x]/4 - (3*x*y[x])/8 - (x*y[x]^2)/4 + (3*x^2*y[x]^2)/16 + y[x]^3/4 - (x*y[x]^3)/2 + (x^2*y[x]^3)/16 - (x^3*y[x]^3)/32)/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {(-1)^{2/3} ((2-3 x) y(x)+6)}{2 \sqrt [3]{29} y(x)}}\frac {1}{K[1]^3+\frac {3 \sqrt [3]{-1} K[1]}{29^{2/3}}+1}dK[1]+\frac {1}{36} (-29)^{2/3} \log (x)=c_1,y(x)\right ] \]