Internal problem ID [5523]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant
Coefficients. Page 62
Problem number: 1(h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }-12 y^{\prime }+9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 18
dsolve(4*diff(y(x),x$2)-12*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {3 x}{2}}+c_{2} {\mathrm e}^{\frac {3 x}{2}} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[4*y''[x]-12*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{3 x/2} (c_2 x+c_1) \\ \end{align*}