Internal problem ID [11767]
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: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {9 y^{\prime \prime }+6 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([9*diff(y(x),x$2)+6*diff(y(x),x)+5*y(x)=0,y(0) = 6, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 3 \,{\mathrm e}^{-\frac {x}{3}} \left (\sin \left (\frac {2 x}{3}\right )+2 \cos \left (\frac {2 x}{3}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 29
DSolve[{9*y''[x]+6*y'[x]+5*y[x]==0,{y[0]==6,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 e^{-x/3} \left (\sin \left (\frac {2 x}{3}\right )+2 \cos \left (\frac {2 x}{3}\right )\right ) \]