Sr Examen
Ecuación diferencial 2sen(x)dy/dx+ycos(x)=y^3(xcos(x)-sen(x))
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Solución
Ha introducido
[src]
d 3
cos(x)*y(x) + 2*--(y(x))*sin(x) = y (x)*(-sin(x) + x*cos(x))
dx
$$y{\left(x \right)} \cos{\left(x \right)} + 2 \sin{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right) y^{3}{\left(x \right)}$$
y*cos(x) + 2*sin(x)*y' = (x*cos(x) - sin(x))*y^3
Respuesta
[src]
______________________________________________________________________________________
/ 1
y(x) = - / ------------------------------------------------------------------------------------
/ / /x\\
/ | x*tan|-||
/ | log(-1 + cos(x)) / /x\\ log(1 + cos(x)) x \2/|
/ |C1 + ---------------- - log|tan|-|| - --------------- + -------- + --------|*sin(x)
/ | 2 \ \2// 2 /x\ 2 |
/ | 2*tan|-| |
\/ \ \2/ /
$$y{\left(x \right)} = - \sqrt{\frac{1}{\left(C_{1} + \frac{x \tan{\left(\frac{x}{2} \right)}}{2} + \frac{x}{2 \tan{\left(\frac{x}{2} \right)}} + \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} - \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}\right) \sin{\left(x \right)}}}$$
______________________________________________________________________________________
/ -1
y(x) = / ------------------------------------------------------------------------------------
/ / /x\ \
/ | x*tan|-| |
/ | log(1 + cos(x)) log(-1 + cos(x)) x \2/ / /x\\|
/ |C1 + --------------- - ---------------- - -------- - -------- + log|tan|-|||*sin(x)
/ | 2 2 /x\ 2 \ \2//|
/ | 2*tan|-| |
\/ \ \2/ /
$$y{\left(x \right)} = \sqrt{- \frac{1}{\left(C_{1} - \frac{x \tan{\left(\frac{x}{2} \right)}}{2} - \frac{x}{2 \tan{\left(\frac{x}{2} \right)}} - \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} + \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}\right) \sin{\left(x \right)}}}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
Bernoulli
lie group
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 18142.609514308937)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 6.397106897951207e+170)
(7.777777777777779, 8.388243566956395e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)