82.17.3 problem Ex. 3

Internal problem ID [18748]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 37
Problem number : Ex. 3
Date solved : Monday, March 31, 2025 at 06:07:34 PM
CAS classification : [_Clairaut]

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

✓ Maple. Time used: 0.263 (sec). Leaf size: 47

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

\begin{align*} y &= \arcsin \left (\frac {\operatorname {RootOf}\left (\textit {\_Z}^{2}-x^{2}+1\right )}{x}\right )-\operatorname {csgn}\left (\frac {1}{x}\right ) \operatorname {RootOf}\left (\textit {\_Z}^{2}-x^{2}+1\right ) \\ y &= c_1 x +\arcsin \left (c_1 \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.17 (sec). Leaf size: 18

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

\begin{align*} y(x)\to \arcsin (c_1)+c_1 x \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

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