Internal problem ID [2146]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=x \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=x*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-2 \,{\mathrm e}^{-x} c_{1} +x^{2}+2 c_{2} -2 x \right ) {\mathrm e}^{-x}}{2} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 35
DSolve[y''[x]+3*y'[x]+2*y[x]==x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-2 x} \left (e^x \left (x^2-2 x+2+2 c_2\right )+2 c_1\right ) \]