Sr Examen
Ecuación diferencial (x/(x^2+y^2)+(2xy)/(x^2+y^2)^2)dx+(1+y/(x^2+y^2)+(y^2-x^2)/(x^2+y^2)^2)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2
x dy*y(x) dy*y (x) dy*x 2*x*y(x) d
---------- + ---------------- + -------------------------------- - -------------------------------- + ----------------------- + --(y(x)) = 0
2 2 2 2 4 4 2 2 4 4 2 2 4 4 2 2 dx
x + y (x) dx*x + dx*y (x) dx*x + dx*y (x) + 2*dx*x *y (x) dx*x + dx*y (x) + 2*dx*x *y (x) x + y (x) + 2*x *y (x)
$$- \frac{dy x^{2}}{dx x^{4} + 2 dx x^{2} y^{2}{\left(x \right)} + dx y^{4}{\left(x \right)}} + \frac{dy y^{2}{\left(x \right)}}{dx x^{4} + 2 dx x^{2} y^{2}{\left(x \right)} + dx y^{4}{\left(x \right)}} + \frac{dy y{\left(x \right)}}{dx x^{2} + dx y^{2}{\left(x \right)}} + \frac{2 x y{\left(x \right)}}{x^{4} + 2 x^{2} y^{2}{\left(x \right)} + y^{4}{\left(x \right)}} + \frac{x}{x^{2} + y^{2}{\left(x \right)}} + \frac{d}{d x} y{\left(x \right)} = 0$$
-dy*x^2/(dx*x^4 + 2*dx*x^2*y^2 + dx*y^4) + dy*y^2/(dx*x^4 + 2*dx*x^2*y^2 + dx*y^4) + dy*y/(dx*x^2 + dx*y^2) + 2*x*y/(x^4 + 2*x^2*y^2 + y^4) + x/(x^2 + y^2) + y' = 0
Clasificación
1st power series
lie group