39.2.3 problem Problem 11.46

Internal problem ID [6520]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.46
Date solved : Monday, January 27, 2025 at 02:11:21 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=4 \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

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

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{x}-2 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 21

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

\[ y(x)\to -2 \sin (x)+e^x (c_2 x+c_1) \]