12.19.11 problem section 9.3, problem 11

Internal problem ID [2158]
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 11
Date solved : Monday, January 27, 2025 at 05:42:55 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y&=2 \,{\mathrm e}^{4 x} \left (13+15 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(y(x),x$3)-7*diff(y(x),x$2)+8*diff(y(x),x)+16*y(x)=2*exp(4*x)*(13+15*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]-7*D[y[x],{x,2}]+8*D[y[x],x]+16*y[x]==2*Exp[4*x]*(13+15*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{4 x} \left (x^3+2 x^2+\left (-\frac {4}{5}+c_3\right ) x+\frac {4}{25}+c_2\right )+c_1 e^{-x} \]