Internal problem ID [11854]
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: 26.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y=x^{2} {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)-diff(y(x),x)+3*y(x)=x^2*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{3 x}-\frac {\left (x^{3}+\frac {3}{2} x -12 c_{1} \right ) {\mathrm e}^{x}}{12} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 41
DSolve[y'''[x]-3*y''[x]-y'[x]+3*y[x]==x^2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (-\frac {x^3}{12}-\frac {x}{8}+c_2\right )+c_1 e^{-x}+c_3 e^{3 x} \]