Internal problem ID [205]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.3, second order linear equations. Page 323
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {9 y^{\prime \prime }+6 y^{\prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 31
dsolve([9*diff(y(x),x$2)+6*diff(y(x),x)+4*y(x)=0,y(0) = 3, D(y)(0) = 4],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{3}} \left (5 \sqrt {3}\, \sin \left (\frac {\sqrt {3}\, x}{3}\right )+3 \cos \left (\frac {\sqrt {3}\, x}{3}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 39
DSolve[{9*y''[x]+6*y'[x]+4*y[x]==0,{y[0]==3,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x/3} \left (5 \sqrt {3} \sin \left (\frac {x}{\sqrt {3}}\right )+3 \cos \left (\frac {x}{\sqrt {3}}\right )\right ) \\ \end{align*}