36.6.4 problem 4

Internal problem ID [6365]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number : 4
Date solved : Monday, January 27, 2025 at 01:58:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 x y^{\prime }-y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 54

Order:=6; 
dsolve((x^2-5*x+6)*diff(y(x),x$2)-3*x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {1}{12} x^{2}+\frac {5}{216} x^{3}+\frac {5}{324} x^{4}+\frac {11}{1296} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{9} x^{3}+\frac {5}{108} x^{4}+\frac {29}{1080} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 63

AsymptoticDSolveValue[(x^2-5*x+6)*D[y[x],{x,2}]-3*x*D[y[x],x]-y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {29 x^5}{1080}+\frac {5 x^4}{108}+\frac {x^3}{9}+x\right )+c_1 \left (\frac {11 x^5}{1296}+\frac {5 x^4}{324}+\frac {5 x^3}{216}+\frac {x^2}{12}+1\right ) \]