Internal problem ID [9802]
Internal file name [OUTPUT/8745_Monday_June_06_2022_05_22_59_AM_91801974/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1476.
ODE order: 3.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_3rd_order, _with_linear_symmetries]]
Unable to solve or complete the solution.
\[ \boxed {27 y^{\prime \prime \prime }-36 n^{2} \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }-2 n \left (n +3\right ) \left (4 n -3\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y=0} \] Unable to solve this ODE.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & 27 \frac {d}{d x}y^{\prime \prime }-36 n^{2} \mathit {WeierstrassP}\left (x , \mathit {g2} , \mathit {g3}\right ) y^{\prime }-2 n \left (n +3\right ) \left (4 n -3\right ) \mathit {WeierstrassPPrime}\left (x , \mathit {g2} , \mathit {g3}\right ) y=0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 3 \\ {} & {} & \frac {d}{d x}y^{\prime \prime } \end {array} \]
Maple trace
`Methods for third order ODEs: --- Trying classification methods --- trying a quadrature checking if the LODE has constant coefficients checking if the LODE is of Euler type trying high order exact linear fully integrable trying to convert to a linear ODE with constant coefficients trying differential order: 3; missing the dependent variable -> pFq: Equivalence to the 3F2 or one of its 3 confluent cases under a power @ Moebius trying a solution in terms of MeijerG functions trying reduction of order using simple exponentials trying differential order: 3; exact nonlinear -> trying with_periodic_functions in the coefficients --- Trying Lie symmetry methods, high order --- `, `-> Computing symmetries using: way = 5`[0, y]
✗ Solution by Maple
dsolve(27*diff(diff(diff(y(x),x),x),x)-36*n^2*WeierstrassP(x,g2,g3)*diff(y(x),x)-2*n*(n+3)*(4*n-3)*WeierstrassPPrime(x,g2,g3)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-2*n*(3 + n)*(-3 + 4*n)*y[x]*Derivative[1][phi][x] - 36*n^2*WeierstrassP[x, {g2, g3}]*y'[x] + 27*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved