Internal problem ID [11830]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 2.
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: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)=tan(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )-2+\sin \left (x \right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 23
DSolve[y''[x]+y[x]==Tan[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x) \text {arctanh}(\sin (x))+c_1 \cos (x)+c_2 \sin (x)-2 \]