Sr Examen
Ecuación diferencial (y^2+y/(cosx)^2)dx+(2xy+tgx)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 y(x) d d
y (x) + ------- + --(y(x))*tan(x) + 2*x*--(y(x))*y(x) = 0
2 dx dx
cos (x)
$$2 x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y^{2}{\left(x \right)} + \frac{y{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \tan{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
2*x*y*y' + y^2 + y/cos(x)^2 + tan(x)*y' = 0
Respuesta
[src]
________________
/ 2
\/ tan (x) + C1*x - tan(x)
y(x) = ----------------------------
2*x
$$y{\left(x \right)} = \frac{\sqrt{C_{1} x + \tan^{2}{\left(x \right)}} - \tan{\left(x \right)}}{2 x}$$
________________
/ 2
- \/ tan (x) + C1*x - tan(x)
y(x) = ------------------------------
2*x
$$y{\left(x \right)} = \frac{- \sqrt{C_{1} x + \tan^{2}{\left(x \right)}} - \tan{\left(x \right)}}{2 x}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 669494.7029799981)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 2.2719528063134115e+184)
(7.777777777777779, 8.38824356697491e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)