Internal problem ID [12215]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 169.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\frac {1}{\cos \left (2 x \right )^{\frac {3}{2}}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 77
dsolve(diff(y(x),x$2)+y(x)=1/(cos(2*x)*sqrt(cos(2*x))),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )+\frac {-\cos \left (x \right )^{2} \sqrt {-2 \sin \left (x \right )^{4}+\sin \left (x \right )^{2}}+\sqrt {\left (2 \cos \left (x \right )^{2}-1\right ) \sin \left (x \right )^{2}}\, \sin \left (x \right )^{2}}{\sqrt {-2 \sin \left (x \right )^{4}+\sin \left (x \right )^{2}}\, \sqrt {2 \cos \left (x \right )^{2}-1}} \]
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 26
DSolve[y''[x]+y[x]==1/(Cos[2*x]*Sqrt[Cos[2*x]]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sqrt {\cos (2 x)}+c_1 \cos (x)+c_2 \sin (x) \]