74.16.1 problem 1

Internal problem ID [16507]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 09:09:55 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 60

Order:=6; 
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+7*y(x)=0,y(x),type='series',x=1);
 

\[ y = \left (1-\frac {7 \left (x -1\right )^{2}}{2}+\frac {35 \left (x -1\right )^{4}}{24}-\frac {7 \left (x -1\right )^{5}}{6}\right ) y \left (1\right )+\left (x -1+\left (x -1\right )^{2}-\frac {5 \left (x -1\right )^{3}}{6}+\frac {7 \left (x -1\right )^{5}}{24}\right ) y^{\prime }\left (1\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 65

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+7*y[x]==0,y[x],{x,1,"6"-1}]
 

\[ y(x)\to c_1 \left (-\frac {7}{6} (x-1)^5+\frac {35}{24} (x-1)^4-\frac {7}{2} (x-1)^2+1\right )+c_2 \left (\frac {7}{24} (x-1)^5-\frac {5}{6} (x-1)^3+(x-1)^2+x-1\right ) \]