38.4.6 problem 6

Internal problem ID [6492]
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 : 6
Date solved : Monday, January 27, 2025 at 02:07:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }+10 y&=20-{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve(diff(y(x),x$2)-diff(y(x),x)+10*y(x)=20-exp(2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {39}\, x}{2}\right ) c_2 +{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {39}\, x}{2}\right ) c_1 +2-\frac {{\mathrm e}^{2 x}}{12} \]

✓ Solution by Mathematica

Time used: 0.988 (sec). Leaf size: 58

DSolve[D[y[x],{x,2}]-D[y[x],x]+10*y[x]==20-Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {e^{2 x}}{12}+c_2 e^{x/2} \cos \left (\frac {\sqrt {39} x}{2}\right )+c_1 e^{x/2} \sin \left (\frac {\sqrt {39} x}{2}\right )+2 \]