50.9.32 problem 5(h)

Internal problem ID [7968]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 5(h)
Date solved : Monday, January 27, 2025 at 03:34:21 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 28

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

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