15.11.10 problem 10

Internal problem ID [3120]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:21:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

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

\[ y = \frac {\left (36 c_2 +6 x -1\right ) {\mathrm e}^{3 x}}{36}+c_{1} {\mathrm e}^{-3 x}-\frac {\sin \left (3 x \right )}{18} \]

✓ Solution by Mathematica

Time used: 0.239 (sec). Leaf size: 39

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

\[ y(x)\to -\frac {1}{18} \sin (3 x)+e^{3 x} \left (\frac {x}{6}-\frac {1}{36}+c_1\right )+c_2 e^{-3 x} \]