49.6.6 problem 1(f)

Internal problem ID [7634]
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)
Date solved : Monday, January 27, 2025 at 03:08:36 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \end{align*}

✓ 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)
 

\[ y = {\mathrm e}^{6 x} c_{2} +{\mathrm e}^{x} c_{1} +\frac {7 \cos \left (x \right )}{74}+\frac {5 \sin \left (x \right )}{74} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]-7*D[y[x],x]+6*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 \sin (x)}{74}+\frac {7 \cos (x)}{74}+c_1 e^x+c_2 e^{6 x} \]