Internal problem ID [1196]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.1 Exercises. Page 318
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x -3 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 2\).
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 54
Order:=6; dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-3*x*y(x)=0,y(x),type='series',x=2);
\[ y \relax (x ) = \left (1+\frac {3 \left (-2+x \right )^{2}}{4}-\frac {3 \left (-2+x \right )^{3}}{8}+\frac {9 \left (-2+x \right )^{4}}{32}-\frac {27 \left (-2+x \right )^{5}}{160}\right ) y \relax (2)+\left (-2+x -\frac {\left (-2+x \right )^{2}}{2}+\frac {\left (-2+x \right )^{3}}{2}-\frac {5 \left (-2+x \right )^{4}}{16}+\frac {31 \left (-2+x \right )^{5}}{160}\right ) D\relax (y )\relax (2)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 87
AsymptoticDSolveValue[x^2*y''[x]+2*x*y'[x]-3*x*y[x]==0,y[x],{x,2,5}]
\[ y(x)\to c_1 \left (-\frac {27}{160} (x-2)^5+\frac {9}{32} (x-2)^4-\frac {3}{8} (x-2)^3+\frac {3}{4} (x-2)^2+1\right )+c_2 \left (\frac {31}{160} (x-2)^5-\frac {5}{16} (x-2)^4+\frac {1}{2} (x-2)^3-\frac {1}{2} (x-2)^2+x-2\right ) \]