35.8.3 problem 3

Internal problem ID [6210]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:47:47 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)+2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +\sin \left (x \right ) {\mathrm e}^{-x} c_{2} +c_3 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 37

DSolve[D[y[x],{x,3}]+2*D[y[x],{x,2}]+2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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