46.1.11 problem 17

Internal problem ID [7301]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page 174
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:49:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 x y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

Order:=6; 
dsolve([diff(y(x),x$2)+3*x*diff(y(x),x)+2*y(x)=0,y(0) = 1, D(y)(0) = 1],y(x),type='series',x=0);
 

\[ y = 1+x -x^{2}-\frac {5}{6} x^{3}+\frac {2}{3} x^{4}+\frac {11}{24} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 32

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

\[ y(x)\to \frac {11 x^5}{24}+\frac {2 x^4}{3}-\frac {5 x^3}{6}-x^2+x+1 \]