Internal problem ID [15106]
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: 218.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(y(x)=diff(y(x),x)*(1+diff(y(x),x)*cos(diff(y(x),x))),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ x -\left (\int _{}^{y \left (x \right )}\frac {1}{\operatorname {RootOf}\left (\cos \left (\textit {\_Z} \right ) \textit {\_Z}^{2}-\textit {\_a} +\textit {\_Z} \right )}d \textit {\_a} \right )-c_{1} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.154 (sec). Leaf size: 38
DSolve[y[x]==y'[x]*(1+y'[x]*Cos[y'[x]]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\log (K[1])+\sin (K[1])+K[1] \cos (K[1])+c_1,y(x)=K[1]+K[1]^2 \cos (K[1])\right \},\{y(x),K[1]\}\right ] \]