Internal problem ID [11760]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }-12 y^{\prime }+9 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 9] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([4*diff(y(x),x$2)-12*diff(y(x),x)+9*y(x)=0,y(0) = 4, D(y)(0) = 9],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {3 x}{2}} \left (3 x +4\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 18
DSolve[{4*y''[x]-12*y'[x]+9*y[x]==0,{y[0]==4,y'[0]==9}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x/2} (3 x+4) \]