52.1.32 problem 28

Internal problem ID [8249]
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. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number : 28
Date solved : Monday, January 27, 2025 at 03:47:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved