Internal problem ID [11746]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients.
Exercises page 135
Problem number: 16.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)+5*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {7}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {7}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 56
DSolve[y'''[x]+4*y''[x]+5*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (c_2 e^{5 x/2} \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 e^{5 x/2} \sin \left (\frac {\sqrt {7} x}{2}\right )+c_3\right ) \]