Internal problem ID [9040]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1461.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-\left (3 k^{2} \mathrm {sn}\left (z | x \right )^{2}+a \right ) y^{\prime }+\left (b +c \mathrm {sn}\left (z | x \right )^{2}-3 k^{2} \mathrm {sn}\left (z | x \right ) \mathrm {cn}\left (z | x \right ) \mathrm {dn}\left (z | x \right )\right ) y=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(diff(y(x),x),x),x)-(3*k^2*JacobiSN(z,x)^2+a)*diff(y(x),x)+(b+c*JacobiSN(z,x)^2-3*k^2*JacobiSN(z,x)*JacobiCN(z,x)*JacobiDN(z,x))*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(b - 3*k^2*JacobiCN[z, x]*JacobiDN[z, x]*JacobiSN[z, x] + c*JacobiSN[z, x]^2)*y[x] - (a + 3*k^2*JacobiSN[z, x]^2)*y'[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved