38.4.10 problem 10

Internal problem ID [6496]
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 : 10
Date solved : Monday, January 27, 2025 at 02:08:43 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)-9*y(x)=exp(3*x)+sin(x),y(x), singsol=all)
 

\[ y = \frac {\left (-1+6 x +36 c_1 \right ) {\mathrm e}^{3 x}}{36}+{\mathrm e}^{-3 x} c_2 -\frac {\sin \left (x \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-9*y[x]==Exp[3*x]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sin (x)}{10}+e^{3 x} \left (\frac {x}{6}-\frac {1}{36}+c_1\right )+c_2 e^{-3 x} \]