75.20.14 problem 653

Internal problem ID [17148]
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 : 653
Date solved : Tuesday, January 28, 2025 at 09:54:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+y(x)=1/sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]+y[x]==1/Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (-x+c_1) \cos (x)+\sin (x) (\log (\sin (x))+c_2) \]