75.8.21 problem 219

Internal problem ID [16766]
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 : 219
Date solved : Monday, March 31, 2025 at 03:16:30 PM
CAS classification : [_quadrature]

\begin{align*} y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 31

ode:=y(x) = arcsin(diff(y(x),x))+ln(1+diff(y(x),x)^2); 
dsolve(ode,y(x), singsol=all);
 

\[ x -\int _{}^{y}\csc \left (\operatorname {RootOf}\left (-\textit {\_a} +\textit {\_Z} +\ln \left (2-\cos \left (\textit {\_Z} \right )^{2}\right )\right )\right )d \textit {\_a} -c_1 = 0 \]

✓ Mathematica. Time used: 0.359 (sec). Leaf size: 46

ode=y[x]==ArcSin[D[y[x],x]]+Log[1+D[y[x],x]^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=2 \arctan (K[1])-\text {arctanh}\left (\sqrt {1-K[1]^2}\right )+c_1,y(x)=\arcsin (K[1])+\log \left (K[1]^2+1\right )\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - log(Derivative(y(x), x)**2 + 1) - asin(Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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