64.11.28 problem 28

Internal problem ID [13478]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 05:44:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 x \,{\mathrm e}^{-3 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)+7*diff(y(x),x)+10*y(x)=4*x*exp(-3*x),y(0) = 0, D(y)(0) = -1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 19

DSolve[{D[y[x],{x,2}]+7*D[y[x],x]+10*y[x]==4*x*Exp[-3*x],{y[0]==0,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

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