15.11.29 problem 29

Internal problem ID [3139]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 29
Date solved : Monday, January 27, 2025 at 07:23:15 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{9}}\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 20

dsolve([diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=x*exp(-x),y(0) = 1/9, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\left (6 x +5\right ) {\mathrm e}^{-x}}{36}-\frac {{\mathrm e}^{x}}{36} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 24

DSolve[{D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==x*Exp[-x],{y[0]==1/9,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{36} e^{-x} \left (-6 x+e^{2 x}-5\right ) \]