75.20.17 problem 656

Internal problem ID [17151]
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 ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 656
Date solved : Tuesday, January 28, 2025 at 09:54:22 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 48

dsolve(diff(y(x),x$2)+y(x)=1/sqrt(sin(x)^5*cos(x)),y(x), singsol=all)
 

\[ y = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\left (\int \frac {\cos \left (x \right )}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}d x \right ) \sin \left (x \right )-\left (\int \frac {\sin \left (x \right )}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}d x \right ) \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]+y[x]==1/Sqrt[Sin[x]^5*Cos[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos (x)+c_2 \sin (x)+\frac {4}{3} \csc ^8(x) \left (\sin ^5(x) \cos (x)\right )^{3/2} \]