38.3.5 problem 5

Internal problem ID [6483]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number : 5
Date solved : Monday, January 27, 2025 at 02:07:32 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 21

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

\[ y(x)\to 2 \cos (x)+e^x (c_2 x+c_1) \]