Internal problem ID [1192]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.1 Exercises. Page 318
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}+1\right ) y^{\prime \prime }+\left (-3 x +2\right ) y^{\prime }+4 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 54
Order:=6; dsolve((1+2*x^2)*diff(y(x),x$2)+(2-3*x)*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-2 x^{2}+\frac {4}{3} x^{3}-\frac {1}{3} x^{4}-\frac {1}{3} x^{5}\right ) y \relax (0)+\left (x -x^{2}+\frac {1}{2} x^{3}-\frac {1}{12} x^{4}-\frac {17}{120} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 66
AsymptoticDSolveValue[(1+2*x^2)*y''[x]+(2-3*x)*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{3}-\frac {x^4}{3}+\frac {4 x^3}{3}-2 x^2+1\right )+c_2 \left (-\frac {17 x^5}{120}-\frac {x^4}{12}+\frac {x^3}{2}-x^2+x\right ) \]