Internal problem ID [11851]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 y \left (x -1\right )=3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x*(x-2)*diff(y(x),x$2)-(x^2-2)*diff(y(x),x)+2*(x-1)*y(x)=3*x^2*(x-2)^2*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{3}-3 x^{2}+c_{1} \right ) {\mathrm e}^{x}+c_{2} x^{2} \]
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 27
DSolve[x*(x-2)*y''[x]-(x^2-2)*y'[x]+2*(x-1)*y[x]==3*x^2*(x-2)^2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^2+e^x \left (x^3-3 x^2+c_1\right ) \]