Internal problem ID [5999]
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]]
\[ \boxed {y^{\prime \prime }-4 y=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-4*y(x)=3*exp(2*x)+4*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\frac {\left (12 x +16 c_{2} -3\right ) {\mathrm e}^{4 x}}{16}+c_{1} -\frac {4 \,{\mathrm e}^{x}}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.345 (sec). Leaf size: 86
DSolve[y''[x]-4*y[x]==3*exp[2*x]+4*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (e^{4 x} \int _1^x\frac {1}{4} e^{-3 K[1]} \left (3 e^{K[1]} \exp (2 K[1])+4\right )dK[1]+\int _1^x-\frac {1}{4} e^{K[2]} \left (3 e^{K[2]} \exp (2 K[2])+4\right )dK[2]+c_1 e^{4 x}+c_2\right ) \]