20.26.1 problem Example 11.5.2 page 763

Internal problem ID [4026]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.5. page 771
Problem number : Example 11.5.2 page 763
Date solved : Monday, January 27, 2025 at 08:06:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 48

Order:=6; 
dsolve(x^2*diff(y(x),x$2)-x*(3+x)*diff(y(x),x)+(4-x)*y(x)=0,y(x),type='series',x=0);
 

\[ y \left (x \right ) = x^{2} \left (\left (\left (-5\right ) x -\frac {29}{4} x^{2}-\frac {173}{36} x^{3}-\frac {193}{96} x^{4}-\frac {1459}{2400} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} +\left (1+3 x +3 x^{2}+\frac {5}{3} x^{3}+\frac {5}{8} x^{4}+\frac {7}{40} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \left (c_{2} \ln \left (x \right )+c_{1} \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 118

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]-x*(3+x)*D[y[x],x]+(4-x)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {7 x^5}{40}+\frac {5 x^4}{8}+\frac {5 x^3}{3}+3 x^2+3 x+1\right ) x^2+c_2 \left (\left (-\frac {1459 x^5}{2400}-\frac {193 x^4}{96}-\frac {173 x^3}{36}-\frac {29 x^2}{4}-5 x\right ) x^2+\left (\frac {7 x^5}{40}+\frac {5 x^4}{8}+\frac {5 x^3}{3}+3 x^2+3 x+1\right ) x^2 \log (x)\right ) \]