75.8.20 problem 218

Internal problem ID [16757]
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
Date solved : Thursday, March 13, 2025 at 08:44:04 AM
CAS classification : [_quadrature]

\begin{align*} y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \end{align*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 33

ode:=y(x) = diff(y(x),x)*(1+diff(y(x),x)*cos(diff(y(x),x))); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ x -\int _{}^{y}\frac {1}{\operatorname {RootOf}\left (\textit {\_Z}^{2} \cos \left (\textit {\_Z} \right )-\textit {\_a} +\textit {\_Z} \right )}d \textit {\_a} -c_{1} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 52

ode=y[x]==D[y[x],x]*(1+D[y[x],x]*Cos[D[y[x],x]]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=\int \frac {K[1]^2 (-\sin (K[1]))+2 K[1] \cos (K[1])+1}{K[1]} \, dK[1]+c_1,y(x)=K[1]+K[1]^2 \cos (K[1])\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-cos(Derivative(y(x), x))*Derivative(y(x), x) - 1)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0, cos(_X0)] 
No algorithms are implemented to solve equation -_X0**2*cos(_X0) - _X0 + y(x)