Internal problem ID [8513]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 933.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {-x^{2}-y x -x^{3}-x y^{2}+2 y x^{2} \ln \relax (x )-\ln \relax (x )^{2} x^{3}-y^{3}+3 x y^{2} \ln \relax (x )-3 x^{2} \ln \relax (x )^{2} y+\ln \relax (x )^{3} x^{3}}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (x ) = \frac {x \left (9 \ln \relax (x )-3+29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right )\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 99
DSolve[y'[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]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {\frac {3 y(x)}{x^2}+\frac {1-3 \log (x)}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {29^{2/3}}{9 \sqrt [3]{\frac {1}{x^3}}}+c_1,y(x)\right ] \]