Internal problem ID [11762]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {9 y^{\prime \prime }-6 y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve([9*diff(y(x),x$2)-6*diff(y(x),x)+y(x)=0,y(0) = 3, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{3}} \left (-2 x +3\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 18
DSolve[{9*y''[x]-6*y'[x]+y[x]==0,{y[0]==3,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{x/3} (3-2 x) \]