19.11 problem section 9.3, problem 11

Internal problem ID [1508]

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.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y-2 \,{\mathrm e}^{4 x} \left (13+15 x \right )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 53

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)
 

\[ y \relax (x ) = \frac {\left (2+x \right ) x^{2} \left (30 \,{\mathrm e}^{4 x} x +26 \,{\mathrm e}^{4 x}\right )}{30 x +26}+{\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{4 x}+c_{3} {\mathrm e}^{4 x} x \]

Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 39

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

\begin{align*} y(x)\to c_1 e^{-x}+e^{4 x} \left (x \left (x (x+2)-\frac {4}{5}+c_3\right )+\frac {4}{25}+c_2\right ) \\ \end{align*}