77.1.29 problem 46 (page 56)

Internal problem ID [17840]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 46 (page 56)
Date solved : Friday, March 14, 2025 at 04:49:36 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime }&=\left (1+y^{2}\right )^{{3}/{2}} \end{align*}

✓ Maple. Time used: 0.677 (sec). Leaf size: 88

ode:=(y(x)-x)*(x^2+1)^(1/2)*diff(y(x),x) = (1+y(x)^2)^(3/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\arctan \left (y\right ) y x -y c_{1} x -\sqrt {\frac {\left (x^{2}+1\right ) \left (1+y^{2}\right )}{\left (x y+1\right )^{2}}}\, y x +\arctan \left (y\right )-y-c_{1} +x -\sqrt {\frac {\left (x^{2}+1\right ) \left (1+y^{2}\right )}{\left (x y+1\right )^{2}}}}{x y+1} = 0 \]

✓ Mathematica. Time used: 1.14 (sec). Leaf size: 57

ode=(y[x]-x)*Sqrt[1+x^2]*D[y[x],x]==(1+y[x]^2)^(3/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x + y(x))*sqrt(x**2 + 1)*Derivative(y(x), x) - (y(x)**2 + 1)**(3/2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out