Internal problem ID [4782]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page
230
Problem number: 16 (x=0).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 49
Order:=6; dsolve((x^2-2*x+10)*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{5} x^{2}+\frac {1}{75} x^{3}+\frac {1}{750} x^{4}-\frac {13}{75000} x^{5}\right ) y \relax (0)+\left (x +\frac {1}{20} x^{3}+\frac {1}{200} x^{4}-\frac {13}{20000} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[(x^2-2*x+10)*y''[x]+x*y'[x]-4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {13 x^5}{20000}+\frac {x^4}{200}+\frac {x^3}{20}+x\right )+c_1 \left (-\frac {13 x^5}{75000}+\frac {x^4}{750}+\frac {x^3}{75}+\frac {x^2}{5}+1\right ) \]