73.17.47 problem 47

Internal problem ID [15581]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 47
Date solved : Tuesday, January 28, 2025 at 08:02:45 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+8 y&={\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 41

dsolve(diff(y(x),x$3)+8*y(x)=exp(-2*x),y(x), singsol=all)
 

\[ y = \frac {\left (12 c_{3} {\mathrm e}^{3 x} \sin \left (\sqrt {3}\, x \right )+12 c_{2} {\mathrm e}^{3 x} \cos \left (\sqrt {3}\, x \right )+12 c_{1} +x \right ) {\mathrm e}^{-2 x}}{12} \]

✓ Solution by Mathematica

Time used: 0.449 (sec). Leaf size: 169

DSolve[D[y[x],{x,3}]+8*y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \sin \left (\sqrt {3} x\right ) \int _1^x\frac {1}{12} e^{-3 K[1]} \left (\sqrt {3} \cos \left (\sqrt {3} K[1]\right )-\sin \left (\sqrt {3} K[1]\right )\right )dK[1]+e^x \cos \left (\sqrt {3} x\right ) \int _1^x-\frac {e^{-3 K[2]} \left (\sqrt {3} \cos \left (\sqrt {3} K[2]\right )+3 \sin \left (\sqrt {3} K[2]\right )\right )}{12 \sqrt {3}}dK[2]+\frac {1}{12} e^{-2 x} x+c_1 e^{-2 x}+c_3 e^x \cos \left (\sqrt {3} x\right )+c_2 e^x \sin \left (\sqrt {3} x\right ) \]