64.13.23 problem 23

Internal problem ID [13553]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 05:52:46 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 y&=4 x -8 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4\\ y^{\prime }\left (1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)-2*y(x)=4*x-8,y(1) = 4, D(y)(1) = -1],y(x), singsol=all)
 

\[ y = x^{2}-2 x +4+\frac {1}{x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 16

DSolve[{x^2*D[y[x],{x,2}]-2*y[x]==4*x-8,{y[1]==4,Derivative[1][y][1]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2-2 x+\frac {1}{x}+4 \]