52.1.23 problem 21

Internal problem ID [8240]
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 : 21
Date solved : Monday, January 27, 2025 at 03:46:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

Order:=8; 
dsolve([diff(y(x),x$2)-2*x*diff(y(x),x)+8*y(x)=0,y(0) = 3, D(y)(0) = 0],y(x),type='series',x=0);
 

\[ y = 4 x^{4}-12 x^{2}+3 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 15

AsymptoticDSolveValue[{D[y[x],{x,2}]-2*x*D[y[x],x]+8*y[x]==0,{y[0]==3,Derivative[1][y][0] ==0}},y[x],{x,0,"8"-1}]
 

\[ y(x)\to 4 x^4-12 x^2+3 \]