Internal problem ID [15424]
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: 659.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\frac {2}{\sin \left (x \right )^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+y(x)=2/sin(x)^3,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} +2 \cot \left (x \right )\right ) \cos \left (x \right )+\sin \left (x \right ) c_{2} -\csc \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 25
DSolve[y''[x]+y[x]==2/Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\csc (x)+c_2 \sin (x)+\cos (x) (2 \cot (x)+c_1) \]