Internal problem ID [11850]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y=x^{3}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x$2)-x*(x+2)*diff(y(x),x)+(x+2)*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = x \left (-x +c_{1} {\mathrm e}^{x}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 22
DSolve[x^2*y''[x]-x*(x+2)*y'[x]+(x+2)*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \left (x-c_2 e^x+1-c_1\right ) \]