15.12.8 problem 8

Internal problem ID [3152]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 8
Date solved : Monday, January 27, 2025 at 07:23:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{x}+\sin \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+9*y(x)=exp(x)+sin(4*x),y(x), singsol=all)
 

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_{1} -\frac {\sin \left (4 x \right )}{7}+\frac {{\mathrm e}^{x}}{10} \]

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]+9*y[x]==Exp[x]+Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x}{10}-\frac {1}{7} \sin (4 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \]