34.1.2 problem 2

Internal problem ID [6026]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 1, Nature and meaning of a differential equation between two variables. page 12
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:33:35 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*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

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

\[ y = x \left (c_1 x +c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 14

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

\[ y(x)\to x (c_2 x+c_1) \]