60.7.31 problem 1621 (6.31)

Internal problem ID [11620]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1621 (6.31)
Date solved : Tuesday, January 28, 2025 at 06:07:04 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime } y-y^{3}+a y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 108

dsolve(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3+a*y(x)=0,y(x), singsol=all)
 

\[ -\frac {\left (\int _{}^{y}\frac {4 {\operatorname {RootOf}\left (\left (-4 \textit {\_a}^{6}+12 \textit {\_a}^{4} a -12 \textit {\_a}^{2} a^{2}+4 a^{3}+320 c_{1} \right ) \textit {\_Z}^{9}+\left (-189 \textit {\_a}^{6}+567 \textit {\_a}^{4} a -567 \textit {\_a}^{2} a^{2}+189 a^{3}+15120 c_{1} \right ) \textit {\_Z}^{6}+238140 c_{1} \textit {\_Z}^{3}+1250235 c_{1} \right )}^{3}+63}{\textit {\_a}^{2}-a}d \textit {\_a} \right )}{63}-x -c_{2} = 0 \]

✓ Solution by Mathematica

Time used: 68.262 (sec). Leaf size: 3100

DSolve[a*y[x] - y[x]^3 + y[x]*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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