28.2.47 problem 47

Internal problem ID [4490]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 47
Date solved : Monday, January 27, 2025 at 09:21:38 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 36

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-4*y(x)=40*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 37

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]-4*y[x]==40*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 \sin (2 x)+\cos (2 x)+e^{-2 x} \left (c_2 x+c_3 e^{3 x}+c_1\right ) \]