60.7.12 problem 1602 (6.12)

Internal problem ID [11601]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1602 (6.12)
Date solved : Monday, January 27, 2025 at 11:24:04 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 61

dsolve(diff(diff(y(x),x),x)+(5+1)*a^(2*5)*y(x)^(2*5+1)-y(x)=0,y(x), singsol=all)
 

\begin{align*} \int _{}^{y}\frac {1}{\sqrt {-\textit {\_a}^{12} a^{10}+\textit {\_a}^{2}+c_{1}}}d \textit {\_a} -x -c_{2} &= 0 \\ -\int _{}^{y}\frac {1}{\sqrt {-\textit {\_a}^{12} a^{10}+\textit {\_a}^{2}+c_{1}}}d \textit {\_a} -x -c_{2} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 10.199 (sec). Leaf size: 49

DSolve[-y[x] + a^(2*5)*(1 + 5)*y[x]^(1 + 2*5) + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+2 \left (\frac {K[1]^2}{2}-\frac {1}{2} a^{10} K[1]^{12}\right )}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]