15.11.22 problem 22

Internal problem ID [3132]
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 : 22
Date solved : Monday, January 27, 2025 at 07:22:36 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+9*y(x)=(1+sin(3*x))*cos(2*x),y(x), singsol=all)
 

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_{1} +\frac {\cos \left (2 x \right )}{5}+\frac {\sin \left (x \right )}{16}-\frac {\sin \left (5 x \right )}{32} \]

✓ Solution by Mathematica

Time used: 0.152 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]+9*y[x]==(1+Sin[3*x])*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (x)}{16}-\frac {1}{32} \sin (5 x)+\frac {1}{5} \cos (2 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \]