45.2.16 problem 16

Internal problem ID [7239]
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 : 16
Date solved : Monday, January 27, 2025 at 02:48:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x y^{\prime \prime }+5 y^{\prime }+y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 32

Order:=6; 
dsolve(2*x*diff(y(x),x$2)+5*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_{1} \left (1-\frac {1}{2} x^{2}+\frac {1}{40} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{{3}/{2}}}+c_{2} \left (1-\frac {1}{14} x^{2}+\frac {1}{616} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 47

AsymptoticDSolveValue[2*x*D[y[x],{x,2}]+5*D[y[x],x]+x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^4}{616}-\frac {x^2}{14}+1\right )+\frac {c_2 \left (\frac {x^4}{40}-\frac {x^2}{2}+1\right )}{x^{3/2}} \]