54.4.21 problem 22

Internal problem ID [8605]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots Nonintegral. Exercises page 365
Problem number : 22
Date solved : Monday, January 27, 2025 at 04:17:16 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 20

Order:=8; 
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);
 

\[ y = \frac {x^{{5}/{2}} c_{2} +c_{1}}{x^{2}}+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 18

AsymptoticDSolveValue[2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]-2*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to \frac {c_2}{x^2}+c_1 \sqrt {x} \]