Internal problem ID [251]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 56.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y=x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-4*y(x)=x*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-9 \,{\mathrm e}^{4 x} c_{2} +3 x \,{\mathrm e}^{3 x}+2 \,{\mathrm e}^{3 x}-9 c_{1} \right ) {\mathrm e}^{-2 x}}{9} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 34
DSolve[y''[x]-4*y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{9} e^x (3 x+2)+c_1 e^{2 x}+c_2 e^{-2 x} \]