Internal problem ID [4357]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{-x} \sin \left (x \right )+c_{3} {\mathrm e}^{-x} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 37
DSolve[y'''[x]+2*y''[x]+2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-x} ((c_2-c_1) \sin (x)-(c_1+c_2) \cos (x))+c_3 \\ \end{align*}