7.11.45 problem 47

Internal problem ID [366]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 47
Date solved : Monday, January 27, 2025 at 02:47:05 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: 0.223 (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]
 

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