28.2.45 problem 45

Internal problem ID [4488]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 45
Date solved : Monday, January 27, 2025 at 09:21:35 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 31

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

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