Mister exam

Differential equation x(y²+1)dx+y(x²+1)dy=0

Differential equation
with unknown function ()

For Cauchy problem:

y() =
y'() =
y''() =
y'''() =
y''''() =

The graph:

from to

The solution

You have entered [src]
       2      d                2 d                
x + x*y (x) + --(y(x))*y(x) + x *--(y(x))*y(x) = 0
              dx                 dx               
$$x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{2}{\left(x \right)} + x + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y*y' + x*y^2 + x + y*y' = 0
The answer [src]
             _________
            /       2 
           /  C1 - x  
y(x) =    /   ------- 
         /          2 
       \/      1 + x  
$$y{\left(x \right)} = \sqrt{\frac{C_{1} - x^{2}}{x^{2} + 1}}$$
              _________
             /       2 
            /  C1 - x  
y(x) = -   /   ------- 
          /          2 
        \/      1 + x  
$$y{\left(x \right)} = - \sqrt{\frac{C_{1} - x^{2}}{x^{2} + 1}}$$
Graph of the Cauchy problem
The classification
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Numerical answer [src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.2515248684038702)
(-5.555555555555555, 1.988129736623045)
(-3.333333333333333, 3.468486206790866)
(-1.1111111111111107, 8.34405797571552)
(1.1111111111111107, 8.34405860084195)
(3.333333333333334, 3.4684861375863703)
(5.555555555555557, 1.9881301767250468)
(7.777777777777779, 1.251525470748332)
(10.0, 0.7500005623827081)
(10.0, 0.7500005623827081)
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