60.2.316 problem 893

Internal problem ID [10903]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 893
Date solved : Tuesday, January 28, 2025 at 05:30:22 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+x^{3} y^{3}+6 x^{2} y^{2}+12 y x +8}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 41

dsolve(diff(y(x),x) = (6*x+x^3+x^3*y(x)^2+4*x^2*y(x)+x^3*y(x)^3+6*x^2*y(x)^2+12*x*y(x)+8)/x^3,y(x), singsol=all)
 

\[ y = \frac {29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1} \right ) x -3 x -18}{9 x} \]

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 58

DSolve[D[y[x],x] == (8 + 6*x + x^3 + 12*x*y[x] + 4*x^2*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^2 + x^3*y[x]^3)/x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {\frac {x+6}{x}+3 y(x)}{\sqrt [3]{29}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ] \]