60.1.187 problem 188

Internal problem ID [10201]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 188
Date solved : Monday, January 27, 2025 at 06:37:48 PM
CAS classification : [[_homogeneous, `class G`], _Abel]

\begin{align*} x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = \operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} a -\textit {\_a} n +b}d \textit {\_a} \right ) x^{n} \]

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 77

DSolve[x^(2*n+1)*D[y[x],x] - a*y[x]^3 - b*x^(3*n)==0,y[x],x,IncludeSingularSolutions -> True]
 

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