Internal problem ID [2216]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=x \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=x*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (4 c_{1} {\mathrm e}^{3 x}+\left (1-2 x \right ) {\mathrm e}^{x}+4 c_{2} \right ) {\mathrm e}^{-2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[y''[x]+y'[x]-2*y[x]==x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-x} (1-2 x)+c_1 e^{-2 x}+c_2 e^x \]