12.12.29 problem 35

Internal problem ID [1883]
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 : 35
Date solved : Monday, January 27, 2025 at 05:37:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

Order:=6; 
dsolve((1+x^3)*diff(y(x),x$2)+7*x^2*diff(y(x),x)+9*x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {3 x^{3}}{2}\right ) y \left (0\right )+\left (x -\frac {4}{3} x^{4}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 28

AsymptoticDSolveValue[(1+x^3)*D[y[x],{x,2}]+7*x^2*D[y[x],x]+9*x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (x-\frac {4 x^4}{3}\right )+c_1 \left (1-\frac {3 x^3}{2}\right ) \]