8.11.17 problem 32

Internal problem ID [885]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 32
Date solved : Monday, January 27, 2025 at 03:14:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

dsolve([diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(x),y(0) = 0, D(y)(0) = 3],y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{3 x}+15 \,{\mathrm e}^{x}-16\right ) {\mathrm e}^{-2 x}}{6} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 26

DSolve[{D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==Exp[x],{y[0]==0,Derivative[1][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{-2 x} \left (15 e^x+e^{3 x}-16\right ) \]