60.2.333 problem 910

Internal problem ID [10920]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 910
Date solved : Tuesday, January 28, 2025 at 05:31:06 PM
CAS classification : [_rational, _Abel]

\begin{align*} y^{\prime }&=\frac {-2 x -y+1+x^{2} y^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x) = (-2*x-y(x)+1+x^2*y(x)^2+2*x^3*y(x)+x^4+x^3*y(x)^3+3*x^4*y(x)^2+3*x^5*y(x)+x^6)/x,y(x), singsol=all)
 

\[ y = \frac {-9 x^{2}+29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1} \right )-3}{9 x} \]

✓ Solution by Mathematica

Time used: 1.185 (sec). Leaf size: 76

DSolve[D[y[x],x] == (1 - 2*x + x^4 + x^6 - y[x] + 2*x^3*y[x] + 3*x^5*y[x] + x^2*y[x]^2 + 3*x^4*y[x]^2 + x^3*y[x]^3)/x,y[x],x,IncludeSingularSolutions -> True]
 

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