60.7.23 problem 1613 (6.23)

Internal problem ID [11612]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1613 (6.23)
Date solved : Tuesday, January 28, 2025 at 06:06:59 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 27

dsolve(diff(diff(y(x),x),x)+5*a*diff(y(x),x)-6*y(x)^2+6*a^2*y(x)=0,y(x), singsol=all)
 

\[ y = \operatorname {WeierstrassP}\left (\frac {-c_{1} a +{\mathrm e}^{-a x}}{a}, 0, c_{2}\right ) {\mathrm e}^{-2 a x} \]

✓ Solution by Mathematica

Time used: 23.409 (sec). Leaf size: 35

DSolve[6*a^2*y[x] - 6*y[x]^2 + 5*a*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to a^2 c_1{}^2 e^{-2 a x} \wp \left (e^{-a x} c_1+c_2;0,-1\right ) \]