Internal problem ID [4641]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of
Parameters
Problem number: Exercise 22.11, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\tan \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)=tan(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+\cos \left (x \right ) c_{1} -2+\ln \left (\sec \left (x \right )+\tan \left (x \right )\right ) \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 23
DSolve[y''[x]+y[x]==Tan[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x) \text {arctanh}(\sin (x))+c_1 \cos (x)+c_2 \sin (x)-2 \]