12.19.10 problem section 9.3, problem 10

Internal problem ID [2157]
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 10
Date solved : Monday, January 27, 2025 at 05:42:54 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y&=2 \,{\mathrm e}^{3 x} \left (11-24 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 35

dsolve(diff(y(x),x$3)-5*diff(y(x),x$2)+3*diff(y(x),x)+9*y(x)=2*exp(3*x)*(11-24*x),y(x), singsol=all)
 

\[ y = \frac {\left (-8 x^{3}+4 x c_3 +17 x^{2}+4 c_2 \right ) {\mathrm e}^{3 x}}{4}+{\mathrm e}^{-x} c_1 \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 46

DSolve[D[y[x],{x,3}]-5*D[y[x],{x,2}]+3*D[y[x],x]+9*y[x]==2*Exp[3*x]*(11-24*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (-2 x^3+\frac {17 x^2}{4}+\left (-\frac {17}{8}+c_3\right ) x+\frac {17}{32}+c_2\right )+c_1 e^{-x} \]