48.3.12 problem Example 3.41

Internal problem ID [7536]
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
Date solved : Monday, January 27, 2025 at 03:04:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=50 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

\[ y = \left (2 \,{\mathrm e}^{5 x}+c_{1} x +c_{2} \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 25

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

\[ y(x)\to e^{-3 x} \left (2 e^{5 x}+c_2 x+c_1\right ) \]