Internal problem ID [11869]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y=2 x^{3}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+8*y(x)=2*x^3,y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (c_{2} x^{2}+c_{1} -2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 21
DSolve[x^2*y''[x]-5*x*y'[x]+8*y[x]==2*x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 \left (c_2 x^2-2 x+c_1\right ) \]