45.2.7 problem 7

Internal problem ID [7230]
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. 6.2 page 239
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:48:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 59

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

\[ y = \left (1-\frac {1}{6} x^{2}-\frac {1}{108} x^{3}-\frac {17}{2592} x^{4}-\frac {7}{2160} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{4} x^{2}+\frac {1}{36} x^{3}+\frac {23}{864} x^{4}+\frac {13}{1440} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 70

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

\[ y(x)\to c_1 \left (-\frac {7 x^5}{2160}-\frac {17 x^4}{2592}-\frac {x^3}{108}-\frac {x^2}{6}+1\right )+c_2 \left (\frac {13 x^5}{1440}+\frac {23 x^4}{864}+\frac {x^3}{36}+\frac {x^2}{4}+x\right ) \]