Internal problem ID [1531]
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 34.
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 }+2 y-{\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \relax (x )-\left (12+12 x \right ) \sin \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 60
dsolve(1*diff(y(x),x$3)-1*diff(y(x),x$2)+0*diff(y(x),x)+2*y(x)=exp(x)*((20+4*x)*cos(x)-(12+12*x)*sin(x)),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {22 \,{\mathrm e}^{x}}{5}+x \,{\mathrm e}^{x}+x^{2} {\mathrm e}^{x}\right ) \cos \relax (x )+\left (\frac {{\mathrm e}^{x}}{5}+3 x \,{\mathrm e}^{x}+x^{2} {\mathrm e}^{x}\right ) \sin \relax (x )+{\mathrm e}^{-x} c_{1}+c_{2} \cos \relax (x ) {\mathrm e}^{x}+c_{3} \sin \relax (x ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.193 (sec). Leaf size: 52
DSolve[1*y'''[x]-1*y''[x]+0*y'[x]+2*y[x]==Exp[x]*((20+4*x)*Cos[x]-(12+12*x)*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^{-x}+\frac {1}{10} e^x ((10 x (x+1)+23+10 c_2) \cos (x)+(10 x (x+3)-21+10 c_1) \sin (x)) \\ \end{align*}