Internal problem ID [15098]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 210.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {-\ln \left (y^{\prime }\right )-\sin \left (y^{\prime }\right )=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x=ln(diff(y(x),x))+sin(diff(y(x),x)),y(x), singsol=all)
\[ y \left (x \right ) = \int \operatorname {RootOf}\left (-x +\ln \left (\textit {\_Z} \right )+\sin \left (\textit {\_Z} \right )\right )d x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 33
DSolve[x==Log[y'[x]]+Sin[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[\{y(x)=K[1]+K[1] \sin (K[1])+\cos (K[1])+c_1,x=\log (K[1])+\sin (K[1])\},\{y(x),K[1]\}] \]