7.8.13 problem 13

Internal problem ID [227]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 13
Date solved : Wednesday, February 05, 2025 at 03:06:14 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 )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.009 (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) = 1],y(x), singsol=all)
 

\[ y = -2 x^{2}+5 x \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 12

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] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (5-2 x) x \]