Internal problem ID [2193]
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: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\sec \left (x \right ) \csc \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 77
dsolve(diff(y(x),x$2)+9*y(x)=sec(x)*csc(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (x \right ) \left (-1+4 \cos \left (x \right )^{2}\right ) \ln \left (\csc \left (x \right )-\cot \left (x \right )\right )}{3}+\frac {\left (4 \cos \left (x \right )^{3}-3 \cos \left (x \right )\right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )}{3}+4 c_{1} \cos \left (x \right )^{3}+4 \cos \left (x \right )^{2} \sin \left (x \right ) c_{2} +\frac {\left (-9 c_{1} +8 \sin \left (x \right )\right ) \cos \left (x \right )}{3}-\sin \left (x \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 65
DSolve[y''[x]+9*y[x]==Sec[x]*Csc[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (\cos (3 x) \text {arctanh}(\sin (x))+4 \sin (2 x)+\sin (3 x) \log \left (\sin \left (\frac {x}{2}\right )\right )+3 c_1 \cos (3 x)+3 c_2 \sin (3 x)-\sin (3 x) \log \left (\cos \left (\frac {x}{2}\right )\right )\right ) \]