Internal problem ID [2161]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+9*y(x)=(1+sin(3*x))*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} +\frac {\cos \left (2 x \right )}{5}+\frac {\sin \left (x \right )}{16}-\frac {\sin \left (5 x \right )}{32} \]
✓ Solution by Mathematica
Time used: 0.266 (sec). Leaf size: 42
DSolve[y''[x]+9*y[x]==(1+Sin[3*x])*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sin (x)}{16}-\frac {1}{32} \sin (5 x)+\frac {1}{5} \cos (2 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \]