Internal problem ID [813]
Internal file name [OUTPUT/813_Sunday_June_05_2022_01_50_25_AM_31574293/index.tex]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.1, Higher order linear differential equations. General theory. page
173
Problem number: 2.
ODE order: 4.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_high_order, _with_linear_symmetries]]
Unable to solve or complete the solution.
\[ \boxed {t \left (-1+t \right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 y t^{2}=0} \] Unable to solve this ODE.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & t \left (-1+t \right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 y t^{2}=0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 4 \\ {} & {} & y^{\prime \prime \prime \prime } \end {array} \]
Maple trace
`Methods for high 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: 4; missing the dependent variable trying a solution in terms of MeijerG functions trying differential order: 4; missing the dependent variable trying a solution in terms of MeijerG functions -> Try computing a Rational Normal Form for the given ODE... <- unable to resolve the Equivalence to a Rational Normal Form trying reduction of order using simple exponentials trying differential order: 4; exact nonlinear --- Trying Lie symmetry methods, high order --- `, `-> Computing symmetries using: way = 3`[0, y]
✗ Solution by Maple
dsolve(t*(t-1)*diff(y(t),t$4)+exp(t)*diff(y(t),t$2)+4*t^2*y(t)=0,y(t), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[t*(t-1)*y''''[t]+Exp[t]*y''[t]+4*t^2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
Not solved