75.20.20 problem 659

Internal problem ID [17154]
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 : 659
Date solved : Tuesday, January 28, 2025 at 09:54:36 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\frac {2}{\sin \left (x \right )^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)+y(x)=2/sin(x)^3,y(x), singsol=all)
 

\[ y = \left (c_{1} +2 \cot \left (x \right )\right ) \cos \left (x \right )+\sin \left (x \right ) c_{2} -\csc \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]+y[x]==2/Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) \int _1^x-2 \csc ^2(K[1])dK[1]-\csc (x)+c_1 \cos (x)+c_2 \sin (x) \]