Internal problem ID [15421]
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: 656.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 48
dsolve(diff(y(x),x$2)+y(x)=1/sqrt(sin(x)^5*cos(x)),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\left (\int \frac {\cos \left (x \right )}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}d x \right ) \sin \left (x \right )-\left (\int \frac {\sin \left (x \right )}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}d x \right ) \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.162 (sec). Leaf size: 35
DSolve[y''[x]+y[x]==1/Sqrt[Sin[x]^5*Cos[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos (x)+c_2 \sin (x)+\frac {4}{3} \csc ^8(x) \left (\sin ^5(x) \cos (x)\right )^{3/2} \]