75.8.12 problem 210

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 : 210
Date solved : Monday, March 31, 2025 at 03:16:07 PM
CAS classification : [_quadrature]

\begin{align*} x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 17

ode:=x = ln(diff(y(x),x))+sin(diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \int \operatorname {RootOf}\left (-x +\ln \left (\textit {\_Z} \right )+\sin \left (\textit {\_Z} \right )\right )d x +c_1 \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 36

ode=x==Log[D[y[x],x]]+Sin[D[y[x],x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

NotImplementedError : multiple generators [log(_X0), sin(_X0)] 
No algorithms are implemented to solve equation x - log(_X0) - sin(_X0)