Internal problem ID [4765]
Book: Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section: Chapter 7. POWER SERIES METHODS. 7.3.2 The method of Frobenius. Exercises. page
300
Problem number: 7.3.6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }+y^{\prime }-x^{2} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.063 (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);
\[ y \relax (x ) = c_{1} \sqrt {x}\, \left (1+\frac {1}{21} x^{3}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1+\frac {1}{15} x^{3}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 33
AsymptoticDSolveValue[2*x*y''[x]+y'[x]-x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (\frac {x^3}{21}+1\right )+c_2 \left (\frac {x^3}{15}+1\right ) \]