45.1.3 problem 16 (x=0)

Internal problem ID [7203]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G. Zill. 9th edition. Brooks/Cole. CA, USA.
Section : Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page 230
Problem number : 16 (x=0)
Date solved : Monday, January 27, 2025 at 02:48:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 54

Order:=6; 
dsolve((x^2-2*x+10)*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {1}{5} x^{2}+\frac {1}{75} x^{3}+\frac {1}{750} x^{4}-\frac {13}{75000} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{20} x^{3}+\frac {1}{200} x^{4}-\frac {13}{20000} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 63

AsymptoticDSolveValue[(x^2-2*x+10)*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (-\frac {13 x^5}{20000}+\frac {x^4}{200}+\frac {x^3}{20}+x\right )+c_1 \left (-\frac {13 x^5}{75000}+\frac {x^4}{750}+\frac {x^3}{75}+\frac {x^2}{5}+1\right ) \]