Internal problem ID [11873]
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: 19.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y=x^{3}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(x^3*diff(y(x),x$3)-x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (4 c_{3} \ln \left (x \right )+4 c_{2} x +x^{2}+4 c_{1} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 29
DSolve[x^3*y'''[x]-x^2*y''[x]+2*x*y'[x]-2*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x \left (x^2+4 c_3 x+4 c_2 \log (x)+4 c_1\right ) \]