3.12 problem Example 3.41

Internal problem ID [5115]

Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number: Example 3.41.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y^{\prime }+9 y-50 \,{\mathrm e}^{2 x}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=50*exp(2*x),y(x), singsol=all)
 

\[ y \relax (x ) = {\mathrm e}^{-3 x} c_{2}+{\mathrm e}^{-3 x} x c_{1}+2 \,{\mathrm e}^{2 x} \]

Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 25

DSolve[y''[x]+6*y'[x]+9*y[x]==50*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-3 x} \left (2 e^{5 x}+c_2 x+c_1\right ) \\ \end{align*}