Internal problem ID [1530]
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 33.
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 }+4 y^{\prime }+12 y-8 \cos \left (2 x \right )+16 \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 43
dsolve(1*diff(y(x),x$3)+3*diff(y(x),x$2)+4*diff(y(x),x)+12*y(x)=8*cos(2*x)-16*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {56}{169}+\frac {8 x}{13}\right ) \cos \left (2 x \right )+\left (\frac {14 x}{13}-\frac {136}{169}\right ) \sin \left (2 x \right )+\cos \left (2 x \right ) c_{1}+c_{2} {\mathrm e}^{-3 x}+c_{3} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 47
DSolve[1*y'''[x]+3*y''[x]+4*y'[x]+12*y[x]==8*Cos[2*x]-16*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{169} \left (169 c_3 e^{-3 x}+(104 x+43+169 c_1) \cos (2 x)+(182 x-32+169 c_2) \sin (2 x)\right ) \\ \end{align*}