Internal problem ID [9122]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1543.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-\left (12 k^{2} \mathrm {sn}\left (z | x \right )^{2}+a \right ) y^{\prime \prime }+y^{\prime } b +\left (\alpha \mathrm {sn}\left (z | x \right )^{2}+\beta \right ) y=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[(\[Beta] + \[Alpha]*JacobiSN[z, x]^2)*y[x] + b*y'[x] - (a + 12*k^2*JacobiSN[z, x]^2)*y''[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved