54.4.23 problem 26

Internal problem ID [8607]
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 : 26
Date solved : Monday, January 27, 2025 at 04:17:19 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*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(2*x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} x^{2}+c_{2} \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[2*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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