Internal problem ID [5210]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 69
Problem number: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+y(x)=tan(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+c_{1} \cos \relax (x )-\cos \relax (x ) \ln \left (\frac {1+\sin \relax (x )}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 49
DSolve[y''[x]+y[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sin (x)+\cos (x) \left (\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_1\right ) \\ \end{align*}