Internal problem ID [2243]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 32.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y-2 \,{\mathrm e}^{-x}-3 \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=2*exp(-x)+3*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-x} x^{3}}{3}+\frac {{\mathrm e}^{2 x}}{9}+{\mathrm e}^{-x} c_{1}+c_{2} x \,{\mathrm e}^{-x}+c_{3} x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 41
DSolve[y'''[x]+3*y''[x]+3*y'[x]+y[x]==2*Exp[-x]+3*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} e^{-x} \left (3 x^3+9 c_3 x^2+e^{3 x}+9 c_2 x+9 c_1\right ) \\ \end{align*}