2.8 problem Problem 1(h)

Internal problem ID [12228]
Internal file name [OUTPUT/10881_Thursday_September_28_2023_01_07_02_AM_86373971/index.tex]

Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number: Problem 1(h).
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, _linear, _nonhomogeneous]]

Unable to solve or complete the solution.

\[ \boxed {y^{\prime \prime \prime }+x y=\cosh \left (x \right )} \] Unable to solve this ODE.

2.8.1 Maple step by step solution

\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & \frac {d}{d x}y^{\prime \prime }+x y=\cosh \left (x \right ) \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 3 \\ {} & {} & \frac {d}{d x}y^{\prime \prime } \end {array} \]

Maple trace

`Methods for third order ODEs: 
--- Trying classification methods --- 
trying a quadrature 
trying high order exact linear fully integrable 
trying differential order: 3; linear nonhomogeneous with symmetry [0,1] 
trying high order linear exact nonhomogeneous 
trying differential order: 3; missing the dependent variable 
checking if the LODE is of Euler type 
trying Louvillian solutions for 3rd order ODEs, imprimitive case 
-> pFq: Equivalence to the 3F2 or one of its 3 confluent cases under a power @ Moebius 
<- pFq successful: received ODE is equivalent to the  0F2  ODE, case  c = 0 `
 

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 1443

dsolve(diff(y(x),x$3)+x*y(x)=cosh(x),y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 91.544 (sec). Leaf size: 2230

DSolve[y'''[x]+x*y[x]==Cosh[x],y[x],x,IncludeSingularSolutions -> True]
 

Too large to display