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xydx+(x^2+y^2)dy=0

Differential equation xydx+(x^2+y^2)dy=0

For Cauchy problem:

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

The graph:

from to

The solution

You have entered [src]
          2 d           2    d           
x*y(x) + x *--(y(x)) + y (x)*--(y(x)) = 0
            dx               dx          
$$x^{2} \frac{d}{d x} y{\left(x \right)} + x y{\left(x \right)} + y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y' + x*y + y^2*y' = 0
The answer [src]
            _____________________
           /           _________ 
          /     2     /       4  
y(x) = -\/   - x  - \/  C1 + x   
$$y{\left(x \right)} = - \sqrt{- x^{2} - \sqrt{C_{1} + x^{4}}}$$
           _____________________
          /           _________ 
         /     2     /       4  
y(x) = \/   - x  - \/  C1 + x   
$$y{\left(x \right)} = \sqrt{- x^{2} - \sqrt{C_{1} + x^{4}}}$$
            ___________________
           /    _________      
          /    /       4     2 
y(x) = -\/   \/  C1 + x   - x  
$$y{\left(x \right)} = - \sqrt{- x^{2} + \sqrt{C_{1} + x^{4}}}$$
           ___________________
          /    _________      
         /    /       4     2 
y(x) = \/   \/  C1 + x   - x  
$$y{\left(x \right)} = \sqrt{- x^{2} + \sqrt{C_{1} + x^{4}}}$$
Graph of the Cauchy problem
The classification
1st exact
1st homogeneous coeff best
1st homogeneous coeff subs indep div dep
1st homogeneous coeff subs dep div indep
1st power series
lie group
1st exact Integral
1st homogeneous coeff subs indep div dep Integral
1st homogeneous coeff subs dep div indep Integral
Numerical answer [src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.9619689990676026)
(-5.555555555555555, 1.3328538606771176)
(-3.333333333333333, 2.063993497553178)
(-1.1111111111111107, 3.075458642648265)
(1.1111111111111107, 3.075458760354001)
(3.333333333333334, 2.063993667128847)
(5.555555555555557, 1.3328537437352466)
(7.777777777777779, 0.9619688864903184)
(10.0, 0.749999949196909)
(10.0, 0.749999949196909)
The graph
Differential equation xydx+(x^2+y^2)dy=0
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