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]]
\[ \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y=-12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
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)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\frac {\left (6 x +3 c_{1} +1\right ) {\mathrm e}^{3 x}}{3}+\cos \left (x \right ) {\mathrm e}^{2 x}+c_{4} {\mathrm e}^{4 x}+\left (x +c_{3} -\frac {1}{6}\right ) {\mathrm e}^{x}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.19 (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]
\[ y(x)\to \cos (x)+c_1 e^{-2 x}+\frac {1}{6} e^{-x} (6 x-1+6 c_2)+\frac {1}{3} e^x (6 x+1+3 c_3)+c_4 e^{2 x} \]