Sr Examen
Ecuación diferencial arctgx(1+y^2)dx=y(1x^2)dy
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Solución
Ha introducido
[src]
2 2 d
y (x)*acot(x) + acot(x) = x *--(y(x))*y(x)
dx
$$y^{2}{\left(x \right)} \operatorname{acot}{\left(x \right)} + \operatorname{acot}{\left(x \right)} = x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
y^2*acot(x) + acot(x) = x^2*y*y'
Respuesta
[src]
____________________________________________
/ 2*acot(x)
/ 2*C1 - --------- 2*acot(x)
/ x 2*C1 - ---------
/ e x
y(x) = - / -1 + ----------------- + e
/ 2
\/ x
$$y{\left(x \right)} = - \sqrt{e^{2 C_{1} - \frac{2 \operatorname{acot}{\left(x \right)}}{x}} - 1 + \frac{e^{2 C_{1} - \frac{2 \operatorname{acot}{\left(x \right)}}{x}}}{x^{2}}}$$
____________________________________________
/ 2*acot(x)
/ 2*C1 - --------- 2*acot(x)
/ x 2*C1 - ---------
/ e x
y(x) = / -1 + ----------------- + e
/ 2
\/ x
$$y{\left(x \right)} = \sqrt{e^{2 C_{1} - \frac{2 \operatorname{acot}{\left(x \right)}}{x}} - 1 + \frac{e^{2 C_{1} - \frac{2 \operatorname{acot}{\left(x \right)}}{x}}}{x^{2}}}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
Bernoulli
almost linear
lie group
separable Integral
1st exact Integral
Bernoulli Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.9260864476032884)
(-5.555555555555555, 1.2353763932870168)
(-3.333333333333333, 2.0185187372957563)
(-1.1111111111111107, 10.742697480712136)
(1.1111111111111107, 6.538918771334893e+26)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 4.3149409499051355e-61)
(7.777777777777779, 8.388243566957444e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)