12.19.5 problem section 9.3, problem 5

Internal problem ID [2152]
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 5
Date solved : Monday, January 27, 2025 at 05:42:52 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 44

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)-3*y(x)=exp(x)*(-1+2*x+24*x^2+16*x^3),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 53

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]-D[y[x],x]-3*y[x]==Exp[x]*(-1+2*x+24*x^2+16*x^3),y[x],x,IncludeSingularSolutions -> True]
 

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