Internal problem ID [9121]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1542.
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 }+a \WeierstrassP \left (x , \mathit {g2} , \mathit {g3}\right ) y^{\prime \prime }+b \WeierstrassPPrime \left (x , \mathit {g2} , \mathit {g3}\right ) y^{\prime }+\left (c \left (6 \WeierstrassP \left (x , \mathit {g2} , \mathit {g3}\right )^{2}-\frac {\mathit {g2}}{2}\right )+d \right ) y=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+a*WeierstrassP(x,g2,g3)*diff(diff(y(x),x),x)+b*WeierstrassPPrime(x,g2,g3)*diff(y(x),x)+(c*(6*WeierstrassP(x,g2,g3)^2-1/2*g2)+d)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(d + c*(-1/2*g2 + 6*WeierstrassP[x, {g2, g3}]^2))*y[x] + b*WeierstrassPPrime[x, {g2, g3}]*y'[x] + a*WeierstrassP[x, {g2, g3}]*y''[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved