2.32 problem Problem 5(f)

Internal problem ID [12252]
Internal file name [OUTPUT/10905_Thursday_September_28_2023_01_08_27_AM_4852287/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 5(f).
ODE order: 2.
ODE degree: 1.

The type(s) of ODE detected by this program : "unknown"

Maple gives the following as the ode type

[[_2nd_order, _linear, _nonhomogeneous]]

Unable to solve or complete the solution.

\[ \boxed {y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y=\tan \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}

Maple trace

`Methods for second order ODEs: 
--- Trying classification methods --- 
trying a quadrature 
trying high order exact linear fully integrable 
trying differential order: 2; linear nonhomogeneous with symmetry [0,1] 
trying a double symmetry of the form [xi=0, eta=F(x)] 
-> Try solving first the homogeneous part of the ODE 
   checking if the LODE has constant coefficients 
   checking if the LODE is of Euler type 
   trying a symmetry of the form [xi=0, eta=F(x)] 
   checking if the LODE is missing y 
   -> Trying a Liouvillian solution using Kovacics algorithm 
   <- No Liouvillian solutions exists 
   -> Trying a solution in terms of special functions: 
      -> Bessel 
      -> elliptic 
      -> Legendre 
      -> Kummer 
         -> hyper3: Equivalence to 1F1 under a power @ Moebius 
      -> hypergeometric 
         -> heuristic approach 
         -> hyper3: Equivalence to 2F1, 1F1 or 0F1 under a power @ Moebius 
         <- hyper3 successful: indirect Equivalence to 0F1 under \`\`^ @ Moebius\`\` is resolved 
      <- hypergeometric successful 
   <- special function solution successful 
<- solving first the homogeneous part of the ODE successful`
 

✓ Solution by Maple

Time used: 1.125 (sec). Leaf size: 522

dsolve([diff(y(x),x$2)-(x-1)*diff(y(x),x)+x^2*y(x)=tan(x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 90.104 (sec). Leaf size: 4228

DSolve[{y''[x]-(x-1)*y'[x]+x^2*y[x]==Tan[x],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

Too large to display