49.11.3 problem 1(c)

Internal problem ID [7667]
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)
Date solved : Monday, January 27, 2025 at 03:09:21 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)-4*y(x)=3*exp(2*x)+4*exp(-x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (\frac {\left (12 x +16 c_{2} -3\right ) {\mathrm e}^{4 x}}{16}+c_{1} -\frac {4 \,{\mathrm e}^{x}}{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.348 (sec). Leaf size: 86

DSolve[D[y[x],{x,2}]-4*y[x]==3*exp[2*x]+4*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^{4 x} \int _1^x\frac {1}{4} e^{-3 K[1]} \left (3 e^{K[1]} \exp (2 K[1])+4\right )dK[1]+\int _1^x-\frac {1}{4} e^{K[2]} \left (3 e^{K[2]} \exp (2 K[2])+4\right )dK[2]+c_1 e^{4 x}+c_2\right ) \]