Internal problem ID [1570]
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 73.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y-30 \cos \relax (x )+10 \sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = -4, y^{\prime \prime }\relax (0) = 16] \end {align*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 25
dsolve([0*diff(y(x),x$4)+1*diff(y(x),x$3)+2*diff(y(x),x$2)+1*diff(y(x),x)+2*y(x)=30*cos(x)-10*sin(x),y(0) = 3, D(y)(0) = -4, (D@@2)(y)(0) = 16],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x}+\left (2-x \right ) \cos \relax (x )+\left (7 x -1\right ) \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 26
DSolve[{0*y''''[x]+1*y'''[x]+2*y''[x]+1*y'[x]+2*y[x]==30*Cos[x]-10*Sin[x],{y[0]==3,y'[0]==-4,y''[0]==16}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x}+(7 x-1) \sin (x)-((x-2) \cos (x)) \\ \end{align*}