Internal problem ID [2427]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.4. page
758
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x \left (-2 x +3\right ) y^{\prime }+\left (1-2 x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 49
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*(3-2*x)*diff(y(x),x)+(1-2*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {\left (2 x +x^{2}+\frac {4}{9} x^{3}+\frac {1}{6} x^{4}+\frac {4}{75} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}+\left (1+\mathrm {O}\left (x^{6}\right )\right ) \left (\ln \relax (x ) c_{2}+c_{1}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 52
AsymptoticDSolveValue[x^2*y''[x]+x*(3-2*x)*y'[x]+(1-2*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {\frac {4 x^5}{75}+\frac {x^4}{6}+\frac {4 x^3}{9}+x^2+2 x}{x}+\frac {\log (x)}{x}\right )+\frac {c_1}{x} \]