60.5.9 problem 1542

Internal problem ID [11543]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1542
Date solved : Monday, January 27, 2025 at 11:23:20 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }+a \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime \prime }+b \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }+\left (c \left (6 \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )^{2}-\frac {\operatorname {g2}}{2}\right )+d \right ) y&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[(d + c*(-1/2*g2 + 6*WeierstrassP[x, {g2, g3}]^2))*y[x] + b*WeierstrassPPrime[x, {g2, g3}]*D[y[x],x] + a*WeierstrassP[x, {g2, g3}]*D[y[x],{x,2}] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved