Internal problem ID [2194]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\csc \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(diff(y(x),x$2)+9*y(x)=csc(2*x),y(x), singsol=all)
\[ y = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} +\frac {\sin \left (x \right ) \left (4 \cos \left (x \right )^{2}-1\right ) \ln \left (\csc \left (x \right )-\cot \left (x \right )\right )}{6}+\frac {2 \left (\left (\cos \left (x \right )^{2}-\frac {3}{4}\right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+2 \sin \left (x \right )\right ) \cos \left (x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 65
DSolve[y''[x]+9*y[x]==Csc[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} \left (\cos (3 x) \text {arctanh}(\sin (x))+4 \sin (2 x)+\sin (3 x) \log \left (\sin \left (\frac {x}{2}\right )\right )+6 c_1 \cos (3 x)+6 c_2 \sin (3 x)-\sin (3 x) \log \left (\cos \left (\frac {x}{2}\right )\right )\right ) \]