28.2.49 problem 49

Internal problem ID [4492]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 49
Date solved : Monday, January 27, 2025 at 09:21:39 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=10 \,{\mathrm e}^{x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=10*exp(x)*sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==10*Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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