Internal problem ID [4823]
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. 6.2 page
239
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 44
Order:=6; dsolve(2*x*diff(y(x),x$2)-(3+2*x)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {5}{2}} \left (1+\frac {4}{7} x +\frac {4}{21} x^{2}+\frac {32}{693} x^{3}+\frac {80}{9009} x^{4}+\frac {64}{45045} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1+\frac {1}{3} x -\frac {1}{6} x^{2}-\frac {1}{6} x^{3}-\frac {5}{72} x^{4}-\frac {7}{360} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 85
AsymptoticDSolveValue[2*x*y''[x]-(3+2*x)*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {7 x^5}{360}-\frac {5 x^4}{72}-\frac {x^3}{6}-\frac {x^2}{6}+\frac {x}{3}+1\right )+c_1 \left (\frac {64 x^5}{45045}+\frac {80 x^4}{9009}+\frac {32 x^3}{693}+\frac {4 x^2}{21}+\frac {4 x}{7}+1\right ) x^{5/2} \]