Internal problem ID [11880]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y=2 x^{3}} \] With initial conditions \begin {align*} [y \left (2\right ) = 0, y^{\prime }\left (2\right ) = -8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+8*y(x)=2*x^3,y(2) = 0, D(y)(2) = -8],y(x), singsol=all)
\[ y \left (x \right ) = -2 x^{3}+4 x^{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 13
DSolve[{x^2*y''[x]-5*x*y'[x]+8*y[x]==2*x^3,{y[2]==0,y'[2]==-8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 (x-2) x^2 \]