Internal problem ID [11877]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y=4 x -8} \] With initial conditions \begin {align*} [y \left (1\right ) = 4, y^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = x^{2}+4-2 x +\frac {1}{x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 16
DSolve[{x^2*y''[x]-2*y[x]==4*x-8,{y[1]==4,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2-2 x+\frac {1}{x}+4 \]