Internal problem ID [7767]
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]
\[ \boxed {x^{1+2 n} y^{\prime }-a y^{3}-b \,x^{3 n}=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} a -\textit {\_a} n +b}d \textit {\_a} \right ) x^{n} \]
✓ Solution by Mathematica
Time used: 0.335 (sec). Leaf size: 331
DSolve[x^(2*n+1)*y'[x] - a*y[x]^3 - b*x^(3*n)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{3} a b^2 \text {RootSum}\left [\text {$\#$1}^9 a b^2+3 \text {$\#$1}^6 a b^2+3 \text {$\#$1}^3 a b^2-\text {$\#$1}^3 n^3+a b^2\&,\frac {\text {$\#$1}^6 \log \left (y(x) \sqrt [3]{\frac {a x^{-3 n}}{b}}-\text {$\#$1}\right )+\text {$\#$1}^4 \sqrt [3]{\frac {n^3}{a b^2}} \log \left (y(x) \sqrt [3]{\frac {a x^{-3 n}}{b}}-\text {$\#$1}\right )+2 \text {$\#$1}^3 \log \left (y(x) \sqrt [3]{\frac {a x^{-3 n}}{b}}-\text {$\#$1}\right )+\text {$\#$1}^2 \left (\frac {n^3}{a b^2}\right )^{2/3} \log \left (y(x) \sqrt [3]{\frac {a x^{-3 n}}{b}}-\text {$\#$1}\right )+\text {$\#$1} \sqrt [3]{\frac {n^3}{a b^2}} \log \left (y(x) \sqrt [3]{\frac {a x^{-3 n}}{b}}-\text {$\#$1}\right )+\log \left (y(x) \sqrt [3]{\frac {a x^{-3 n}}{b}}-\text {$\#$1}\right )}{3 \text {$\#$1}^8 a b^2+6 \text {$\#$1}^5 a b^2+3 \text {$\#$1}^2 a b^2-\text {$\#$1}^2 n^3}\&\right ]=b x^n \log (x) \sqrt [3]{\frac {a x^{-3 n}}{b}}+c_1,y(x)\right ] \]