12.19.8 problem section 9.3, problem 8

Internal problem ID [2155]
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 8
Date solved : Monday, January 27, 2025 at 05:42:53 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{x} \left (7+6 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 31

dsolve(diff(y(x),x$3)-diff(y(x),x$2)-diff(y(x),x)+y(x)=-exp(x)*(7+6*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 41

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]-D[y[x],x]+y[x]==-Exp[x]*(7+6*x),y[x],x,IncludeSingularSolutions -> True]
 

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