Internal problem ID [11790]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 16.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y=9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)-diff(y(x),x)+2*y(x)=9*exp(2*x)-8*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (3 x +c_{3} -4\right ) {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}-{\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 44
DSolve[y'''[x]-2*y''[x]-y'[x]+2*y[x]==9*Exp[2*x]-8*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{3 x}+c_1 e^{-x}+\left (\frac {81}{32}+c_2\right ) e^x+e^{2 x} (3 x-4+c_3) \]