Internal problem ID [5213]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 69
Problem number: 1(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-7 y^{\prime }+6 y-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-7*diff(y(x),x)+6*y(x)=sin(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{6 x} c_{1}+\frac {7 \cos \relax (x )}{74}+\frac {5 \sin \relax (x )}{74} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 32
DSolve[y''[x]-7*y'[x]+6*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {5 \sin (x)}{74}+\frac {7 \cos (x)}{74}+c_1 e^x+c_2 e^{6 x} \\ \end{align*}