Internal problem ID [1546]
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 49.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y-5 \,{\mathrm e}^{2 x}-2 \,{\mathrm e}^{x}+4 \cos \relax (x )-4 \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 41
dsolve(1*diff(y(x),x$3)-1*diff(y(x),x$2)+1*diff(y(x),x)-1*y(x)=5*exp(2*x)+2*exp(x)-4*cos(x)+4*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \left (2 x +2\right ) \cos \relax (x )+x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}-2 \sin \relax (x )-{\mathrm e}^{x}+c_{1} \cos \relax (x )+c_{2} {\mathrm e}^{x}+c_{3} \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 35
DSolve[1*y'''[x]-1*y''[x]+1*y'[x]-1*y[x]==5*Exp[2*x]+2*Exp[x]-4*Cos[x]+4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (x+e^x-1+c_3\right )+(2 x+1+c_1) \cos (x)+(-2+c_2) \sin (x) \\ \end{align*}