Sr Examen
Ecuación diferencial 2(x+y)dx+(2x-2y+1)dy=0
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Solución
Ha introducido
[src]
d d d
2*x + 2*y(x) - 2*--(y(x))*y(x) + 2*x*--(y(x)) + --(y(x)) = 0
dx dx dx
$$2 x \frac{d}{d x} y{\left(x \right)} + 2 x - 2 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$
2*x*y' + 2*x - 2*y*y' + 2*y + y' = 0
Respuesta
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/ 2
1 \/ C1 + 4*x + 8*x
y(x) = - + x - --------------------
2 2
$$y{\left(x \right)} = x - \frac{\sqrt{C_{1} + 8 x^{2} + 4 x}}{2} + \frac{1}{2}$$
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/ 2
1 \/ C1 + 4*x + 8*x
y(x) = - + x + --------------------
2 2
$$y{\left(x \right)} = x + \frac{\sqrt{C_{1} + 8 x^{2} + 4 x}}{2} + \frac{1}{2}$$
Clasificación
1st exact
linear coefficients
1st power series
lie group
1st exact Integral
linear coefficients Integral