45.1.12 problem 24

Internal problem ID [7212]
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 : 24
Date solved : Monday, January 27, 2025 at 02:48:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 33

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

\[ y = \left (1+\frac {1}{4} x^{2}-\frac {1}{24} x^{3}+\frac {1}{480} x^{5}\right ) y \left (0\right )+y^{\prime }\left (0\right ) x +O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 34

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

\[ y(x)\to c_1 \left (\frac {x^5}{480}-\frac {x^3}{24}+\frac {x^2}{4}+1\right )+c_2 x \]