Internal problem ID [8654]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1074.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {k^{2} \mathrm {sn}\left (x | k \right ) \mathrm {cn}\left (x | k \right ) y^{\prime }}{\mathrm {dn}\left (x | k \right )}+n^{2} y \mathrm {dn}\left (x | k \right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(diff(y(x),x),x)+k^2*JacobiSN(x,k)*JacobiCN(x,k)/JacobiDN(x,k)*diff(y(x),x)+n^2*y(x)*JacobiDN(x,k)^2=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (n \,\mathrm {am}\left (x | k \right )\right )+c_{2} \cos \left (n \,\mathrm {am}\left (x | k \right )\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[n^2*JacobiDN[x, k]^2*y[x] + (k^2*JacobiCN[x, k]*JacobiSN[x, k]*y'[x])/JacobiDN[x, k] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved