54.4.19 problem 20

Internal problem ID [8603]
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 : 20
Date solved : Monday, January 27, 2025 at 04:17:14 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 19

Order:=8; 
dsolve(2*x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
 

\[ y = \sqrt {x}\, c_{1} +c_{2} x^{2}+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 18

AsymptoticDSolveValue[2*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+2*y[x]==0,y[x],{x,0,"8"-1}]
 

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