12.19.60 problem section 9.3, problem 60

Internal problem ID [2207]
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 60
Date solved : Monday, January 27, 2025 at 05:43:34 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&={\mathrm e}^{2 x} \left (10+3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(diff(y(x),x$3)-1*diff(y(x),x$2)-1*diff(y(x),x)+1*y(x)=exp(2*x)*(10+3*x),y(x), singsol=all)
 

\[ y = \left (x +1\right ) {\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-x}+{\mathrm e}^{x} \left (x c_3 +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]-1*D[y[x],{x,2}]-1*D[y[x],x]+1*y[x]==Exp[2*x]*(10+3*x),y[x],x,IncludeSingularSolutions -> True]
 

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