Internal problem ID [4736]
Book: Advanced Mathemtical Methods for Scientists and Engineers, Bender and Orszag. Springer
October 29, 1999
Section: Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page
136
Problem number: 3.24 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }-y^{\prime }+y x^{2}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 28
Order:=6; dsolve(2*x*diff(y(x),x$2)-diff(y(x),x)+x^2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {3}{2}} \left (1-\frac {1}{27} x^{3}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1-\frac {1}{9} x^{3}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 33
AsymptoticDSolveValue[2*x*y''[x]-y'[x]+x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (1-\frac {x^3}{9}\right )+c_1 \left (1-\frac {x^3}{27}\right ) x^{3/2} \]