Internal problem ID [1235]
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: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (-x^{3}+1\right ) y^{\prime \prime }+15 y^{\prime } x^{2}-36 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
Order:=6; dsolve((1-x^3)*diff(y(x),x$2)+15*x^2*diff(y(x),x)-36*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (6 x^{3}+1\right ) y \relax (0)+\left (x +\frac {7}{4} x^{4}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 28
AsymptoticDSolveValue[(1-2*x^3)*y''[x]-10*x^2*y'[x]-8*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {3 x^4}{2}+x\right )+c_1 \left (\frac {4 x^3}{3}+1\right ) \]