Sr Examen
Ecuación diferencial xdx/dy-(1+x²)y=xy²
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Solución
Ha introducido
[src]
2 x y(x) x *y(x) 2 -- - ---- - ------- = x*y (x) dy dx dx
$$\frac{x}{dy} - \frac{x^{2} y{\left(x \right)}}{dx} - \frac{y{\left(x \right)}}{dx} = x y^{2}{\left(x \right)}$$
x/dy - x^2*y/dx - y/dx = x*y^2
Respuesta
[src]
/ ______________________________________ \
| / / 4 2 2 2\ / 2\|
-\\/ dy*\dy + dy*x + 2*dy*x + 4*dx *x / + dy*\1 + x //
y(x) = -----------------------------------------------------------
2*dx*dy*x
$$y{\left(x \right)} = - \frac{dy \left(x^{2} + 1\right) + \sqrt{dy \left(4 dx^{2} x^{2} + dy x^{4} + 2 dy x^{2} + dy\right)}}{2 dx dy x}$$
______________________________________
/ / 4 2 2 2\ / 2\
\/ dy*\dy + dy*x + 2*dy*x + 4*dx *x / - dy*\1 + x /
y(x) = -------------------------------------------------------
2*dx*dy*x
$$y{\left(x \right)} = \frac{- dy \left(x^{2} + 1\right) + \sqrt{dy \left(4 dx^{2} x^{2} + dy x^{4} + 2 dy x^{2} + dy\right)}}{2 dx dy x}$$
Clasificación
nth algebraic
nth algebraic Integral