73.16.17 problem 24.3 (a)

Internal problem ID [15529]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.3 (a)
Date solved : Tuesday, January 28, 2025 at 08:01:22 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime }&=30 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$3)-4*diff(y(x),x)=30*exp(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (4 \,{\mathrm e}^{5 x}+{\mathrm e}^{4 x} c_{1} +2 c_{3} {\mathrm e}^{2 x}-c_{2} \right ) {\mathrm e}^{-2 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 37

DSolve[D[y[x],{x,3}]-4*D[y[x],x]==30*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

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