12.19.54 problem section 9.3, problem 54

Internal problem ID [2201]
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
Date solved : Monday, January 27, 2025 at 05:43:28 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=-12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = {\mathrm e}^{-2 x} \left (\frac {\left (6 x +3 c_1 +1\right ) {\mathrm e}^{3 x}}{3}+{\mathrm e}^{2 x} \cos \left (x \right )+c_4 \,{\mathrm e}^{4 x}+\left (x +c_3 -\frac {1}{6}\right ) {\mathrm e}^{x}+c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 58

DSolve[D[y[x],{x,4}]-0*D[y[x],{x,3}]-5*D[y[x],{x,2}]-0*D[y[x],x]+4*y[x]==-12*Exp[x]+6*Exp[-x]+10*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x)+c_1 e^{-2 x}+\frac {1}{6} e^{-x} (6 x-1+6 c_2)+\frac {1}{3} e^x (6 x+1+3 c_3)+c_4 e^{2 x} \]