Internal problem ID [15431]
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: 666.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+y^{\prime } \tan \left (x \right )=\cot \left (x \right ) \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)+tan(x)*diff(y(x),x)=cos(x)*cot(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} +\sin \left (x \right ) \left (-1+\ln \left (\sin \left (x \right )\right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 39
DSolve[y''[x]+Tan[x]*y'[x]==Cos[x]*Cot[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \sqrt {\sin ^2(x)} \log \left (\sin ^2(x)\right )-(1+c_2) \sqrt {\sin ^2(x)}+c_1 \]