60.1.555 problem 568

Internal problem ID [10569]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 568
Date solved : Sunday, March 30, 2025 at 06:07:47 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y&=0 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 32

ode:=diff(y(x),x)^2*sin(diff(y(x),x))-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ x -\int _{}^{y}\frac {1}{\operatorname {RootOf}\left (\sin \left (\textit {\_Z} \right ) \textit {\_Z}^{2}-\textit {\_a} \right )}d \textit {\_a} -c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 47

ode=-y[x] + Sin[D[y[x],x]]*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + sin(Derivative(y(x), x))*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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