Internal problem ID [2195]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\tan \left (\frac {x}{3}\right )^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 48
dsolve(diff(y(x),x$2)+y(x)=tan(x/3)^2,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -22+9 \sin \left (\frac {x}{3}\right ) \left (1-4 \cos \left (\frac {x}{3}\right )^{2}\right ) \ln \left (\sec \left (\frac {x}{3}\right )+\tan \left (\frac {x}{3}\right )\right )+36 \cos \left (\frac {x}{3}\right )^{2} \]
✓ Solution by Mathematica
Time used: 0.283 (sec). Leaf size: 36
DSolve[y''[x]+y[x]==Tan[x/3]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -9 \sin (x) \text {arctanh}\left (\sin \left (\frac {x}{3}\right )\right )+18 \cos \left (\frac {2 x}{3}\right )+c_1 \cos (x)+c_2 \sin (x)-4 \]