Internal problem ID [11789]
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: 15.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y=4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+4*y(x)=4*exp(x)-18*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-6 x +3 c_{1} -4\right ) {\mathrm e}^{-x}}{3}+\left (c_{3} x +c_{2} \right ) {\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 44
DSolve[y'''[x]-3*y''[x]+4*y[x]==4*Exp[x]-18*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-x} \left (-6 x+6 e^{2 x}+3 e^{3 x} (c_3 x+c_2)-4+3 c_1\right ) \]