Sr Examen
Ecuación diferencial dx*(x/sqrt(x^2+y^2)+y)+dy*(x+y/sqrt(x^2+y^2))=0
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Solución
Ha introducido
[src]
d
--(y(x))*y(x)
x d dx
--------------- + x*--(y(x)) + --------------- + y(x) = 0
____________ dx ____________
/ 2 2 / 2 2
\/ x + y (x) \/ x + y (x)
$$x \frac{d}{d x} y{\left(x \right)} + \frac{x}{\sqrt{x^{2} + y^{2}{\left(x \right)}}} + y{\left(x \right)} + \frac{y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}}{\sqrt{x^{2} + y^{2}{\left(x \right)}}} = 0$$
x*y' + x/sqrt(x^2 + y^2) + y + y*y'/sqrt(x^2 + y^2) = 0
Respuesta
[src]
_______________
/ 2 4 2
- \/ C1 + x - x + C1*x
y(x) = ---------------------------
2
-1 + x
$$y{\left(x \right)} = \frac{C_{1} x - \sqrt{C_{1}^{2} + x^{4} - x^{2}}}{x^{2} - 1}$$
_______________
/ 2 4 2
\/ C1 + x - x + C1*x
y(x) = -------------------------
2
-1 + x
$$y{\left(x \right)} = \frac{C_{1} x + \sqrt{C_{1}^{2} + x^{4} - x^{2}}}{x^{2} - 1}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral