Internal problem ID [11918]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.2 (Frobenius).
Exercises page 251
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 44
Order:=6; dsolve((2*x^2-x)*diff(y(x),x$2)+(2*x-2)*diff(y(x),x)+(-2*x^2+3*x-2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} \left (1-x +\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (1-2 x +\frac {7}{2} x^{2}-\frac {4}{3} x^{3}+\frac {13}{24} x^{4}-\frac {7}{60} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 60
AsymptoticDSolveValue[(2*x^2-x)*y''[x]+(2*x-2)*y'[x]+(-2*x^2+3*x-2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {7 x^3}{8}-\frac {7 x^2}{3}+\frac {11 x}{2}+\frac {1}{x}-4\right )+c_2 \left (\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \]