12.12.30 problem 36

Internal problem ID [1884]
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 : 36
Date solved : Monday, January 27, 2025 at 05:37:48 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 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((1-2*x^3)*diff(y(x),x$2)+6*x^2*diff(y(x),x)+24*x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (-4 x^{3}+1\right ) y \left (0\right )+\left (x -\frac {5}{2} x^{4}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 26

AsymptoticDSolveValue[(1-2*x^3)*D[y[x],{x,2}]+6*x^2*D[y[x],x]+24*x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (x-\frac {5 x^4}{2}\right )+c_1 \left (1-4 x^3\right ) \]