8.11.24 problem 47

Internal problem ID [892]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 47
Date solved : Monday, January 27, 2025 at 03:16:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=4*exp(x),y(x), singsol=all)
 

\[ y = -\left (-c_2 \,{\mathrm e}^{x}+c_1 -\frac {2 \,{\mathrm e}^{3 x}}{3}\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==4*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

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