45.3.17 problem 19

Internal problem ID [7275]
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 : 19
Date solved : Monday, January 27, 2025 at 02:49:31 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+x^{3} 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: 28

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

\[ y = c_{1} \left (1-\frac {1}{24} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-2+\frac {1}{4} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 30

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

\[ y(x)\to c_2 \left (1-\frac {x^4}{24}\right )+c_1 \left (\frac {1}{x^2}-\frac {x^2}{8}\right ) \]