64.1.14 problem 6(b)

Internal problem ID [13259]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 6(b)
Date solved : Tuesday, January 28, 2025 at 05:13:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=-8 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=-8*sin(2*x),y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{2 x}-\cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==-8*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\cos (2 x)+e^{2 x} (c_2 x+c_1) \]