Internal problem ID [2168]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=x \,{\mathrm e}^{-x}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{9}}, y^{\prime }\left (0\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
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)
\[ y \left (x \right ) = \frac {\left (6 x +5\right ) {\mathrm e}^{-x}}{36}-\frac {{\mathrm e}^{x}}{36} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 24
DSolve[{y''[x]-3*y'[x]+2*y[x]==x*Exp[-x],{y[0]==1/9,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{36} e^{-x} \left (-6 x+e^{2 x}-5\right ) \]