Internal problem ID [9020]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1441.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {2 \,\mathrm {sn}\left (x | k \right ) \mathrm {cn}\left (x | k \right ) \mathrm {dn}\left (x | k \right ) y^{\prime }-2 \left (1-2 \left (k^{2}+1\right ) \mathrm {sn}\left (a | k \right )^{2}+3 k^{2} \mathrm {sn}\left (a | k \right )^{4}\right ) y}{\mathrm {sn}\left (x | k \right )^{2}-\mathrm {sn}\left (a | k \right )}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x) = (2*JacobiSN(x,k)*JacobiCN(x,k)*JacobiDN(x,k)*diff(y(x),x)-2*(1-2*(k^2+1)*JacobiSN(a,k)^2+3*k^2*JacobiSN(a,k)^4)*y(x))/(JacobiSN(x,k)^2-JacobiSN(a,k)),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == -(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2)^(-1) - ((2 - 4*(1 + k^2)*JacobiSN[a, k]^2 + 6*k^2*JacobiSN[a, k]^4)*y[x])/(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2) - ((-(JacobiCN[x, k]*JacobiDN[x, k]) - 2*JacobiSN[x, k])*y'[x])/(-JacobiSN[a, k]^2 + JacobiSN[x, k]^2),y[x],x,IncludeSingularSolutions -> True]
Not solved