Internal problem ID [4763]
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: 7.3.5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}-x y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
Order:=6; dsolve(diff(y(x),x$2)+1/x*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (\ln \left (x \right ) c_{2} +c_{1} \right ) \left (1+\frac {1}{9} x^{3}+\operatorname {O}\left (x^{6}\right )\right )+\left (-\frac {2}{27} x^{3}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 39
AsymptoticDSolveValue[y''[x]+1/x*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^3}{9}+1\right )+c_2 \left (\left (\frac {x^3}{9}+1\right ) \log (x)-\frac {2 x^3}{27}\right ) \]