Internal problem ID [1549]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined
Coefficients for Higher Order Equations. Page 495
Problem number: section 9.3, problem 52.
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-12 \,{\mathrm e}^{-x}-9 \cos \left (2 x \right )+13 \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 46
dsolve(1*diff(y(x),x$3)+3*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=12*exp(-x)+9*cos(2*x)-13*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = 2 \,{\mathrm e}^{-x} x^{3}-\cos \left (2 x \right )+\sin \left (2 x \right )+{\mathrm e}^{-x} c_{1}+x \,{\mathrm e}^{-x} c_{2}+c_{3} x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 38
DSolve[1*y'''[x]+3*y''[x]+3*y'[x]+1*y[x]==12*Exp[-x]+9*Cos[2*x]-13*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (2 x)-\cos (2 x)+e^{-x} (x (x (2 x+c_3)+c_2)+c_1) \\ \end{align*}