73.17.23 problem 23

Internal problem ID [15557]
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 : 23
Date solved : Tuesday, January 28, 2025 at 08:02:00 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }&=8 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 50

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)=8,y(x), singsol=all)
 

\[ y = \frac {\left (-\frac {\sqrt {3}\, c_{2}}{3}+c_{1} \right ) {\mathrm e}^{3 x} \cos \left (\sqrt {3}\, x \right )}{4}+\frac {{\mathrm e}^{3 x} \left (\sqrt {3}\, c_{1} +3 c_{2} \right ) \sin \left (\sqrt {3}\, x \right )}{12}+\frac {2 x}{3}+c_{3} \]

✓ Solution by Mathematica

Time used: 60.045 (sec). Leaf size: 55

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]==8,y[x],x,IncludeSingularSolutions -> True]
 

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