64.8.6 problem 9

Internal problem ID [13394]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:41:39 AM
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 (1\right )&=3\\ y^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve([x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(1) = 3, D(y)(1) = 2],y(x), singsol=all)
 

\[ y = -x^{2}+4 x \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 11

DSolve[{x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+2*y[x]==0,{y[1]==3,Derivative[1][y][1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -((x-4) x) \]