50.15.1 problem 3

Internal problem ID [8067]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Challenge excercises. Page 105
Problem number : 3
Date solved : Monday, January 27, 2025 at 03:41:20 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 11

DSolve[{x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+2*y[x]==0,{y[0]==0,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^2 \]