Sr Examen
Ecuación diferencial dx*(2*x*y-sec(2*x))+dy*(x^2+2*y)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d d
-sec(2*x) + x *--(y(x)) + 2*x*y(x) + 2*--(y(x))*y(x) = 0
dx dx
$$x^{2} \frac{d}{d x} y{\left(x \right)} + 2 x y{\left(x \right)} + 2 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - \sec{\left(2 x \right)} = 0$$
x^2*y' + 2*x*y + 2*y*y' - sec(2*x) = 0
Respuesta
[src]
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2 / 4
x \/ C1 + x - log(-1 + sin(2*x)) + log(1 + sin(2*x))
y(x) = - -- - -----------------------------------------------------
2 2
$$y{\left(x \right)} = - \frac{x^{2}}{2} - \frac{\sqrt{C_{1} + x^{4} - \log{\left(\sin{\left(2 x \right)} - 1 \right)} + \log{\left(\sin{\left(2 x \right)} + 1 \right)}}}{2}$$
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/ 4 2
\/ C1 + x - log(-1 + sin(2*x)) + log(1 + sin(2*x)) x
y(x) = ----------------------------------------------------- - --
2 2
$$y{\left(x \right)} = - \frac{x^{2}}{2} + \frac{\sqrt{C_{1} + x^{4} - \log{\left(\sin{\left(2 x \right)} - 1 \right)} + \log{\left(\sin{\left(2 x \right)} + 1 \right)}}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.2033179354084094)
(-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, 1.7373559329555976e-47)
(7.777777777777779, 8.388243566958928e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)