45.3.18 problem 20

Internal problem ID [7276]
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. 6.3.1 page 250
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:49:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

Order:=6; 
dsolve(9*x^2*diff(y(x),x$2)+9*x*diff(y(x),x)+(x^6-36)*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} x^{2} \left (1+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-144+\operatorname {O}\left (x^{6}\right )\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 16

AsymptoticDSolveValue[9*x^2*D[y[x],{x,2}]+9*x*D[y[x],x]+(x^6-36)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 x^2+\frac {c_1}{x^2} \]