Internal problem ID [13610]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises.
page 641
Problem number: 33.5 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
Order:=6; dsolve((x^2-6*x)*diff(y(x),x$2)+4*(x-3)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} \left (1+\frac {1}{6} x +\frac {1}{36} x^{2}+\frac {1}{216} x^{3}+\frac {1}{1296} x^{4}+\frac {1}{7776} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (1+\frac {1}{3} x +\frac {1}{18} x^{2}+\frac {1}{108} x^{3}+\frac {1}{648} x^{4}+\frac {1}{3888} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 64
AsymptoticDSolveValue[(x^2-6*x)*y''[x]+4*(x-3)*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^3}{1296}+\frac {x^2}{216}+\frac {x}{36}+\frac {1}{x}+\frac {1}{6}\right )+c_2 \left (\frac {x^4}{1296}+\frac {x^3}{216}+\frac {x^2}{36}+\frac {x}{6}+1\right ) \]