75.4.22 problem 87

Internal problem ID [16653]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 87
Date solved : Monday, March 31, 2025 at 03:03:43 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

\[ y = x \arcsin \left (x \right )+\sqrt {-x^{2}+1}+c_1 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 23

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

\[ y(x)\to x \arcsin (x)+\sqrt {1-x^2}+c_1 \]

✓ Sympy. Time used: 0.230 (sec). Leaf size: 37

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

\[ \left [ y{\left (x \right )} = C_{1} - x \operatorname {asin}{\left (x \right )} + \pi x - \sqrt {1 - x^{2}}, \ y{\left (x \right )} = C_{1} + x \operatorname {asin}{\left (x \right )} + \sqrt {1 - x^{2}}\right ] \]