Sr Examen
Ecuación diferencial xsqrt(9-y^2)dx-y(4+x^2)dy=0
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Solución
Ha introducido
[src]
___________
/ 2 d 2 d
x*\/ 9 - y (x) - 4*--(y(x))*y(x) - x *--(y(x))*y(x) = 0
dx dx
$$- x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x \sqrt{9 - y^{2}{\left(x \right)}} - 4 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-x^2*y*y' + x*sqrt(9 - y^2) - 4*y*y' = 0
Respuesta
[src]
______________________________________________
/ 2/ 2\ 2 / 2\
-\/ 36 - log \4 + x / - 4*C1 - 4*C1*log\4 + x /
y(x) = ---------------------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{- 4 C_{1}^{2} - 4 C_{1} \log{\left(x^{2} + 4 \right)} - \log{\left(x^{2} + 4 \right)}^{2} + 36}}{2}$$
______________________________________________
/ 2/ 2\ 2 / 2\
\/ 36 - log \4 + x / - 4*C1 - 4*C1*log\4 + x /
y(x) = -------------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{- 4 C_{1}^{2} - 4 C_{1} \log{\left(x^{2} + 4 \right)} - \log{\left(x^{2} + 4 \right)}^{2} + 36}}{2}$$
Clasificación
factorable
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral