45.3.23 problem 25

Internal problem ID [7281]
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 : 25
Date solved : Monday, January 27, 2025 at 02:49:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\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: 32

Order:=6; 
dsolve(16*x^2*diff(y(x),x$2)+32*x*diff(y(x),x)+(x^4-12)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_{1} x^{2} \left (1-\frac {1}{384} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (-2+\frac {1}{64} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 40

AsymptoticDSolveValue[16*x^2*D[y[x],{x,2}]+32*x*D[y[x],x]+(x^4-12)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {1}{x^{3/2}}-\frac {x^{5/2}}{128}\right )+c_2 \left (\sqrt {x}-\frac {x^{9/2}}{384}\right ) \]