28.2.50 problem 50

Internal problem ID [4493]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 50
Date solved : Monday, January 27, 2025 at 09:21:39 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }-4 y&=50 \sin \left (x \right )+50 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 38

dsolve(diff(y(x),x$3)-2*diff(y(x),x)-4*y(x)=50*(sin(x)+exp(2*x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{1} +5 x -3\right ) {\mathrm e}^{2 x}+\left (c_{2} \cos \left (x \right )+c_3 \sin \left (x \right )\right ) {\mathrm e}^{-x}+6 \cos \left (x \right )-8 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 47

DSolve[D[y[x],{x,3}]-2*D[y[x],x]-4*y[x]==50*(Sin[x]+Exp[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{3 x} (5 x-3+c_3)+\left (6 e^x+c_2\right ) \cos (x)+\left (-8 e^x+c_1\right ) \sin (x)\right ) \]