Internal problem ID [11798]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\sin \left (x \right ) y+y^{\prime } \cos \left (x \right )=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(y(x)*sin(x)+diff(y(x),x)*cos(x)=1,y(x), singsol=all)
\[ y \left (x \right ) = \left (\tan \left (x \right )+c_{1} \right ) \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 13
DSolve[y[x]*Sin[x]+y'[x]*Cos[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x)+c_1 \cos (x) \]