12.19.50 problem section 9.3, problem 50

Internal problem ID [2197]
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 50
Date solved : Monday, January 27, 2025 at 05:43:25 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 41

dsolve(1*diff(y(x),x$3)-0*diff(y(x),x$2)-1*diff(y(x),x)-0*y(x)=-2*(1+x)+4*exp(x)-6*exp(-x)+96*exp(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (-6 x -2 c_1 -9\right ) {\mathrm e}^{-x}}{2}+4 \,{\mathrm e}^{3 x}+\left (2 x -3+c_2 \right ) {\mathrm e}^{x}+x^{2}+2 x +c_3 \]

✓ Solution by Mathematica

Time used: 0.608 (sec). Leaf size: 49

DSolve[1*D[y[x],{x,3}]-0*D[y[x],{x,2}]-1*D[y[x],x]-0*y[x]==-2*(1+x)+4*Exp[x]-6*Exp[-x]+96*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (x+2)+4 e^{3 x}+e^x (2 x-3+c_1)-\frac {1}{2} e^{-x} (6 x+9+2 c_2)+c_3 \]