50.13.18 problem 17

Internal problem ID [8033]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 17
Date solved : Monday, January 27, 2025 at 03:36:58 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+2*diff(y(x),x)=10+42*exp(3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_{2} +\frac {{\mathrm e}^{2 x} c_{1}}{2}+7 \,{\mathrm e}^{3 x}+5 x +c_3 \]

✓ Solution by Mathematica

Time used: 0.268 (sec). Leaf size: 35

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+2*D[y[x],x]==10+42*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 x+7 e^{3 x}+c_1 e^x+\frac {1}{2} c_2 e^{2 x}+c_3 \]