60.4.13 problem 1461

Internal problem ID [11464]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1461
Date solved : Monday, January 27, 2025 at 11:22:25 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-\left (3 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime }+\left (b +c \operatorname {JacobiSN}\left (z , x\right )^{2}-3 k^{2} \operatorname {JacobiSN}\left (z , x\right ) \operatorname {JacobiCN}\left (z , x\right ) \operatorname {JacobiDN}\left (z , x\right )\right ) y&=0 \end{align*}

✗ 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: 0.000 (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)*D[y[x],x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved