12.19.4 problem section 9.3, problem 4

Internal problem ID [2151]
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 4
Date solved : Monday, January 27, 2025 at 05:42:51 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 34

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)-3*y(x)=exp(-2*x)*(2-17*x+3*x^2),y(x), singsol=all)
 

\[ y = \left (c_3 \,{\mathrm e}^{2 x}+{\mathrm e}^{4 x} c_1 +\left (x^{2}-5 x +1\right ) {\mathrm e}^{x}+c_2 \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]-D[y[x],x]-3*y[x]==Exp[-2*x]*(2-17*x+3*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (e^x \left (x^2-5 x+1\right )+c_2 e^{2 x}+c_3 e^{4 x}+c_1\right ) \]