20.9.22 problem Problem 22

Internal problem ID [3766]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 22
Date solved : Monday, January 27, 2025 at 08:01:05 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=12 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+9*diff(y(x),x)=12*exp(3*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (4+18 x^{2}+3 \left (c_{1} -4\right ) x -c_{1} +3 c_{2} \right ) {\mathrm e}^{3 x}}{9}+c_3 \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 39

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+9*D[y[x],x]==12*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} e^{3 x} \left (18 x^2+3 (-4+c_2) x+4+3 c_1-c_2\right )+c_3 \]