Sr Examen
Ecuación diferencial dx*(x*y^2+y)+dy*(x^2*y+x-1)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 d 2 d - --(y(x)) + x*y (x) + x*--(y(x)) + x *--(y(x))*y(x) + y(x) = 0 dx dx dx
$$x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{2}{\left(x \right)} + x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} - \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y*y' + x*y^2 + x*y' + y - y' = 0
Respuesta
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______________________
/ 2 2
1 \/ 1 + x - 2*x + C1*x
-1 + - - -------------------------
x x
y(x) = ----------------------------------
x
$$y{\left(x \right)} = \frac{-1 - \frac{\sqrt{C_{1} x^{2} + x^{2} - 2 x + 1}}{x} + \frac{1}{x}}{x}$$
______________________
/ 2 2
1 \/ 1 + x - 2*x + C1*x
-1 + - + -------------------------
x x
y(x) = ----------------------------------
x
$$y{\left(x \right)} = \frac{-1 + \frac{\sqrt{C_{1} x^{2} + x^{2} - 2 x + 1}}{x} + \frac{1}{x}}{x}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral