Internal problem ID [7768]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 188.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _Abel]
Solve \begin {gather*} \boxed {x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 32
dsolve(x^(2*n+1)*diff(y(x),x) - a*y(x)^3 - b*x^(3*n)=0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\ln \relax (x )+c_{1}+\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} a -n \textit {\_a} +b}d \textit {\_a} \right ) x^{n} \]
✓ Solution by Mathematica
Time used: 0.169 (sec). Leaf size: 105
DSolve[x^(2*n+1)*y'[x] - a*y[x]^3 - b*x^(3*n)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\text {RootSum}\left [-\text {$\#$1}^3+\text {$\#$1} \sqrt [3]{\frac {n^3}{a b^2}}-1\&,\frac {\log \left (y(x) \sqrt [3]{\frac {a x^{-3 n}}{b}}-\text {$\#$1}\right )}{\sqrt [3]{\frac {n^3}{a b^2}}-3 \text {$\#$1}^2}\&\right ]=b x^n \log (x) \sqrt [3]{\frac {a x^{-3 n}}{b}}+c_1,y(x)\right ] \]