Internal problem ID [5246]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 93
Problem number: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y-3 \,{\mathrm e}^{2 x}-4 \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-4*y(x)=3*exp(2*x)+4*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{-2 x}+\frac {\left (36 x -9\right ) {\mathrm e}^{2 x}}{48}-\frac {4 \,{\mathrm e}^{-x}}{3} \]
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 81
DSolve[y''[x]-4*y[x]==3*exp[2*x]+4*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (\int _1^x-\frac {1}{4} e^{K[2]} \left (3 e^{K[2]} \exp (2 K[2])+4\right )dK[2]+e^{4 x} \left (\int _1^x\frac {1}{4} e^{-3 K[1]} \left (3 e^{K[1]} \exp (2 K[1])+4\right )dK[1]+c_1\right )+c_2\right ) \\ \end{align*}