60.5.10 problem 1543

Internal problem ID [11544]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1543
Date solved : Monday, January 27, 2025 at 11:23:21 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-\left (12 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime \prime }+b y^{\prime }+\left (\alpha \operatorname {JacobiSN}\left (z , x\right )^{2}+\beta \right ) y&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-(12*k^2*JacobiSN(z,x)^2+a)*diff(diff(y(x),x),x)+b*diff(y(x),x)+(alpha*JacobiSN(z,x)^2+beta)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(\[Beta] + \[Alpha]*JacobiSN[z, x]^2)*y[x] + b*D[y[x],x] - (a + 12*k^2*JacobiSN[z, x]^2)*D[y[x],{x,2}] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved