Sr Examen
Ecuación diferencial sqrt(4+y^2)dx-ydy=x^2ydy
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Solución
Ha introducido
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/ 2 d 2 d
\/ 4 + y (x) - --(y(x))*y(x) = x *--(y(x))*y(x)
dx dx
$$\sqrt{y^{2}{\left(x \right)} + 4} - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
sqrt(y^2 + 4) - y*y' = x^2*y*y'
Respuesta
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/ 2 2
y(x) = -\/ -4 + C1 + atan (x) + 2*C1*atan(x)
$$y{\left(x \right)} = - \sqrt{C_{1}^{2} + 2 C_{1} \operatorname{atan}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)} - 4}$$
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/ 2 2
y(x) = \/ -4 + C1 + atan (x) + 2*C1*atan(x)
$$y{\left(x \right)} = \sqrt{C_{1}^{2} + 2 C_{1} \operatorname{atan}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)} - 4}$$
Clasificación
factorable
separable
1st power series
lie group
separable Integral