45.2.23 problem 23

Internal problem ID [7246]
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 : 23
Date solved : Monday, January 27, 2025 at 02:48:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 47

Order:=6; 
dsolve(9*x^2*diff(y(x),x$2)+9*x^2*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} x^{{1}/{3}} \left (1-\frac {1}{2} x +\frac {1}{5} x^{2}-\frac {7}{120} x^{3}+\frac {7}{528} x^{4}-\frac {13}{5280} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{{2}/{3}} \left (1-\frac {1}{2} x +\frac {5}{28} x^{2}-\frac {1}{21} x^{3}+\frac {11}{1092} x^{4}-\frac {11}{6240} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 90

AsymptoticDSolveValue[9*x^2*D[y[x],{x,2}]+9*x^2*D[y[x],x]+2*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \sqrt [3]{x} \left (-\frac {13 x^5}{5280}+\frac {7 x^4}{528}-\frac {7 x^3}{120}+\frac {x^2}{5}-\frac {x}{2}+1\right )+c_1 x^{2/3} \left (-\frac {11 x^5}{6240}+\frac {11 x^4}{1092}-\frac {x^3}{21}+\frac {5 x^2}{28}-\frac {x}{2}+1\right ) \]