Internal problem ID [13654]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional
Exercises. page 715
Problem number: 35.2 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
Order:=6; dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{1} \sqrt {x}+c_{2} x}{x^{\frac {3}{2}}}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 18
AsymptoticDSolveValue[2*x^2*y''[x]+5*x*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_1}{\sqrt {x}}+\frac {c_2}{x} \]