Internal problem ID [12534]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 168.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sec \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+y(x)=sec(x),y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (\sec \left (x \right )\right ) \cos \left (x \right )+c_{1} \cos \left (x \right )+\sin \left (x \right ) \left (c_{2} +x \right ) \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 22
DSolve[y''[x]+y[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (x+c_2) \sin (x)+\cos (x) (\log (\cos (x))+c_1) \]