12.12.37 problem 44

Internal problem ID [1891]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN ORDINARY POINT I. Exercises 7.2. Page 329
Problem number : 44
Date solved : Monday, January 27, 2025 at 05:37:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 15

Order:=6; 
dsolve(diff(y(x),x$2)+x^5*diff(y(x),x)+6*x^4*y(x)=0,y(x),type='series',x=0);
 

\[ y = y \left (0\right )+y^{\prime }\left (0\right ) x +O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 10

AsymptoticDSolveValue[D[y[x],{x,2}]+x^5*D[y[x],x]+6*x^4*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 x+c_1 \]