Internal problem ID [5381]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 15. Linear equations with constant coefficients (Variation of parameters).
Supplemetary problems. Page 98
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=4 \sec \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
dsolve(diff(y(x),x$2)+4*y(x)=4*sec(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \left (-8 \cos \left (x \right )^{2}+4\right ) \ln \left (\sec \left (x \right )\right )+2 c_{1} \cos \left (x \right )^{2}+8 \left (x +\frac {c_{2}}{4}\right ) \sin \left (x \right ) \cos \left (x \right )-4 \sin \left (x \right )^{2}-c_{1} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 44
DSolve[y''[x]+4*y[x]==4*Sec[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 \sin (2 x) \arctan (\tan (x))+2 x \sin (2 x)+c_2 \sin (2 x)+\cos (2 x) (4 \log (\cos (x))+2+c_1)-2 \]