45.1.19 problem 31

Internal problem ID [7219]
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. 6.1.2 page 230
Problem number : 31
Date solved : Monday, January 27, 2025 at 02:48:22 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: 14

Order:=6; 
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);
 

\[ y = 3-12 x^{2}+4 x^{4}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 22

AsymptoticDSolveValue[{D[y[x],{x,2}]-2*x*D[y[x],{x,2}]+8*y[x]==0,{y[0]==3,Derivative[1][y][0] ==0}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {16 x^5}{5}-8 x^3-12 x^2+3 \]