Internal problem ID [1202]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x^{2} \left (3 x +1\right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 44
Order:=6; dsolve(x^2*(1+3*x)*diff(y(x),x$2)+x*(2+12*x+x^2)*diff(y(x),x)+2*x*(3+x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \left (1-3 x +\frac {26}{3} x^{2}-\frac {101}{4} x^{3}+\frac {4441}{60} x^{4}-\frac {26141}{120} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (1-6 x +\frac {35}{2} x^{2}-\frac {101}{2} x^{3}+\frac {1177}{8} x^{4}-\frac {17251}{40} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 60
AsymptoticDSolveValue[x^2*(1+3*x)*y''[x]+x*(2+12*x+x^2)*y'[x]+2*x*(3+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {571 x^3}{8}-\frac {49 x^2}{2}+\frac {17 x}{2}+\frac {1}{x}-3\right )+c_2 \left (\frac {4441 x^4}{60}-\frac {101 x^3}{4}+\frac {26 x^2}{3}-3 x+1\right ) \]