29.37.16 problem 1135

Internal problem ID [5674]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1135
Date solved : Sunday, March 30, 2025 at 09:59:06 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.107 (sec). Leaf size: 32

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

\begin{align*} y &= 1 \\ x -\int _{}^{y}\frac {1}{\operatorname {RootOf}\left (\textit {\_Z} \sin \left (\textit {\_Z} \right )+\cos \left (\textit {\_Z} \right )-\textit {\_a} \right )}d \textit {\_a} -c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 31

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

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

✗ Sympy

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

NotImplementedError : multiple generators [_X0, tan(_X0/2)] 
No algorithms are implemented to solve equation 2*_X0*tan(_X0/2)/(tan(_X0/2)**2 + 1) + (1 - tan(_X0/2)**2)/(tan(_X0/2)**2 + 1) - y(x)