Internal problem ID [15420]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 655.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\frac {1}{\cos \left (x \right )^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+y(x)=1/cos(x)^3,y(x), singsol=all)
\[ y \left (x \right ) = \left (-1+c_{1} \right ) \cos \left (x \right )+\sin \left (x \right ) c_{2} +\frac {\sec \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 25
DSolve[y''[x]+y[x]==1/Cos[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sec (x)}{2}+c_1 \cos (x)+\sin (x) (\tan (x)+c_2) \]