Internal problem ID [243]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 48.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-8 y=3 \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=3*exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{4 x} c_{2} +{\mathrm e}^{-2 x} c_{1} -\frac {{\mathrm e}^{-2 x} x}{2} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 32
DSolve[y''[x]-2*y'[x]-8*y[x]==3*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} e^{-2 x} \left (-6 x+12 c_2 e^{6 x}-1+12 c_1\right ) \]