Internal problem ID [6394]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 3(h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\tan \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+4*y(x)=tan(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \left (2 \cos \left (x \right )^{2}-1\right ) \ln \left (\cos \left (x \right )\right )+2 c_{1} \cos \left (x \right )^{2}+2 \left (x +c_{2} \right ) \sin \left (x \right ) \cos \left (x \right )-\frac {3 \sin \left (x \right )^{2}}{2}-c_{1} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 32
DSolve[y''[x]+4*y[x]==Tan[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (x+c_2) \sin (2 x)+\cos (2 x) \left (\log (\cos (x))+\frac {1}{4}+c_1\right )-\frac {3}{4} \]