Internal problem ID [12535]
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: 21
dsolve(diff(y(x),x$2)+y(x)=1/(cos(2*x)*sqrt(cos(2*x))),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )-\sqrt {\cos \left (2 x \right )} \]
✓ 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]
\[ y(x)\to -\sqrt {\cos (2 x)}+c_1 \cos (x)+c_2 \sin (x) \]