Internal problem ID [15061]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 168.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
\[ \boxed {\cos \left (y\right ) y^{\prime }+\sin \left (y\right )=x +1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(diff(y(x),x)*cos(y(x))+sin(y(x))=x+1,y(x), singsol=all)
\[ y \left (x \right ) = -\arcsin \left (-x +c_{1} {\mathrm e}^{-x}\right ) \]
✓ Solution by Mathematica
Time used: 13.261 (sec). Leaf size: 17
DSolve[y'[x]*Cos[y[x]]+Sin[y[x]]==x+1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arcsin \left (x-c_1 e^{-x}\right ) \]