38.4.3 problem 3

Internal problem ID [6489]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 3
Date solved : Monday, January 27, 2025 at 02:07:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=100 \sin \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=100*sin(4*x),y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_1 +4 \cos \left (4 x \right )-2 \sin \left (4 x \right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==100*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 \sin (4 x)+4 \cos (4 x)+e^{2 x} \left (c_2 e^x+c_1\right ) \]