Internal problem ID [1551]
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 54.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y+12 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}-10 \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 66
dsolve(diff(y(x),x$4)-0*diff(y(x),x$3)-5*diff(y(x),x$2)-0*diff(y(x),x)+4*y(x)=-12*exp(x)+6*exp(-x)+10*cos(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (-2 \,{\mathrm e}^{4 x}-6 \,{\mathrm e}^{3 x} \cos \relax (x )+{\mathrm e}^{2 x}-12 \,{\mathrm e}^{4 x} x -6 \,{\mathrm e}^{2 x} x \right ) {\mathrm e}^{-3 x}}{6}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x}+c_{4} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 58
DSolve[y''''[x]-0*y'''[x]-5*y''[x]-0*y'[x]+4*y[x]==-12*Exp[x]+6*Exp[-x]+10*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (x)+\frac {1}{6} e^{-2 x} \left (e^x \left (6 x+2 e^{2 x} \left (6 x+3 c_4 e^x+1+3 c_3\right )-1+6 c_2\right )+6 c_1\right ) \\ \end{align*}