82.6.1 problem 33-1 (a)

Internal problem ID [21848]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 33. Systems of ordinary differential equations. Page 1059
Problem number : 33-1 (a)
Date solved : Thursday, October 02, 2025 at 08:02:51 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \sqrt {1-y^{2}}+\left (x +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 41

ode:=(1-y(x)^2)^(1/2)+(2*y(x)+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x +2 \,{\mathrm e}^{-\arcsin \left (y\right )} \int _{}^{y}\frac {\textit {\_a} \,{\mathrm e}^{\arcsin \left (\textit {\_a} \right )}}{\sqrt {-\textit {\_a}^{2}+1}}d \textit {\_a} -{\mathrm e}^{-\arcsin \left (y\right )} c_1 = 0 \]

✓ Mathematica. Time used: 0.175 (sec). Leaf size: 32

ode=Sqrt[1-y[x]^2]+(x+2*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.609 (sec). Leaf size: 37

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

\[ C_{1} + x e^{\operatorname {asin}{\left (y{\left (x \right )} \right )}} - \sqrt {1 - y^{2}{\left (x \right )}} e^{\operatorname {asin}{\left (y{\left (x \right )} \right )}} + y{\left (x \right )} e^{\operatorname {asin}{\left (y{\left (x \right )} \right )}} = 0 \]