52.2.16 problem 16

Internal problem ID [8267]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number : 16
Date solved : Monday, January 27, 2025 at 03:47:28 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: 0.014 (sec). Leaf size: 36

Order:=8; 
dsolve(2*x*diff(y(x),x$2)+5*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_{1} \left (1-\frac {1}{2} x^{2}+\frac {1}{40} x^{4}-\frac {1}{2160} x^{6}+\operatorname {O}\left (x^{8}\right )\right )}{x^{{3}/{2}}}+c_{2} \left (1-\frac {1}{14} x^{2}+\frac {1}{616} x^{4}-\frac {1}{55440} x^{6}+\operatorname {O}\left (x^{8}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 61

AsymptoticDSolveValue[2*x*D[y[x],{x,2}]+5*D[y[x],x]+x*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 \left (-\frac {x^6}{55440}+\frac {x^4}{616}-\frac {x^2}{14}+1\right )+\frac {c_2 \left (-\frac {x^6}{2160}+\frac {x^4}{40}-\frac {x^2}{2}+1\right )}{x^{3/2}} \]