Sr Examen
Ecuación diferencial x*(x^2+y^2)*dx=2*y*sqrt(x^2+4)*(x*dy-y*dx)
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Solución
Ha introducido
[src]
________ ________
3 2 / 2 2 / 2 d
x + x*y (x) = - 2*\/ 4 + x *y (x) + 2*x*\/ 4 + x *--(y(x))*y(x)
dx
$$x^{3} + x y^{2}{\left(x \right)} = 2 x \sqrt{x^{2} + 4} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 2 \sqrt{x^{2} + 4} y^{2}{\left(x \right)}$$
x^3 + x*y^2 = 2*x*sqrt(x^2 + 4)*y*y' - 2*sqrt(x^2 + 4)*y^2
Respuesta
[src]
___________________
/ /x\
/ asinh|-|
/ \2/
y(x) = -x*\/ -1 + C1*e
$$y{\left(x \right)} = - x \sqrt{C_{1} e^{\operatorname{asinh}{\left(\frac{x}{2} \right)}} - 1}$$
___________________
/ /x\
/ asinh|-|
/ \2/
y(x) = x*\/ -1 + C1*e
$$y{\left(x \right)} = x \sqrt{C_{1} e^{\operatorname{asinh}{\left(\frac{x}{2} \right)}} - 1}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
Bernoulli
almost linear
lie group
1st exact Integral
Bernoulli Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 4.15110233947315)
(-5.555555555555555, 4.882486000269447)
(-3.333333333333333, 4.48825762915795)
(-1.1111111111111107, 2.4784808160649474)
(1.1111111111111107, -4.480404731536125)
(3.333333333333334, -19.90693003103377)
(5.555555555555557, -42.014689718780126)
(7.777777777777779, -69.2504214521993)
(10.0, -100.77887244850295)
(10.0, -100.77887244850295)