60.2.356 problem 933

Internal problem ID [10943]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 933
Date solved : Tuesday, January 28, 2025 at 05:34:59 PM
CAS classification : [_Abel]

\begin{align*} y^{\prime }&=-\frac {-x^{2}-y x -x^{3}-x y^{2}+2 y x^{2} \ln \left (x \right )-x^{3} \ln \left (x \right )^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

dsolve(diff(y(x),x) = -(-x^2-x*y(x)-x^3-x*y(x)^2+2*y(x)*x^2*ln(x)-x^3*ln(x)^2-y(x)^3+3*x*y(x)^2*ln(x)-3*x^2*ln(x)^2*y(x)+x^3*ln(x)^3)/x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.229 (sec). Leaf size: 77

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

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