Internal problem ID [14888]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 67.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 27
Order:=6; dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {x^{\frac {5}{2}} c_{2} +c_{1}}{x^{2}}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 18
AsymptoticDSolveValue[2*x^2*y''[x]+5*x*y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_2}{x^2}+c_1 \sqrt {x} \]