Sr Examen
Ecuación diferencial sin(y)^2-y'*x^14=0
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Solución
Ha introducido
[src]
2 14 d
sin (y(x)) - x *--(y(x)) = 0
dx
$$- x^{14} \frac{d}{d x} y{\left(x \right)} + \sin^{2}{\left(y{\left(x \right)} \right)} = 0$$
-x^14*y' + sin(y)^2 = 0
Respuesta
[src]
/ _______________________________________\
| / 26 13 2 26 |
| 1 \/ 1 + 169*x - 26*C1*x + 169*C1 *x |
y(x) = -2*atan|-C1 + ------ + ------------------------------------------|
| 13 13 |
\ 13*x 13*x /
$$y{\left(x \right)} = - 2 \operatorname{atan}{\left(- C_{1} + \frac{\sqrt{169 C_{1}^{2} x^{26} - 26 C_{1} x^{13} + 169 x^{26} + 1}}{13 x^{13}} + \frac{1}{13 x^{13}} \right)}$$
/ _______________________________________\
| / 26 13 2 26 |
| 1 \/ 1 + 169*x - 26*C1*x + 169*C1 *x |
y(x) = 2*atan|C1 - ------ + ------------------------------------------|
| 13 13 |
\ 13*x 13*x /
$$y{\left(x \right)} = 2 \operatorname{atan}{\left(C_{1} + \frac{\sqrt{169 C_{1}^{2} x^{26} - 26 C_{1} x^{13} + 169 x^{26} + 1}}{13 x^{13}} - \frac{1}{13 x^{13}} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.7500000001546171)
(-5.555555555555555, 0.7500000006348064)
(-3.333333333333333, 0.7500000201584146)
(-1.1111111111111107, 0.7591748553112694)
(1.1111111111111107, 3.1415926809250987)
(3.333333333333334, 3.1415926809250987)
(5.555555555555557, 3.1415926809250987)
(7.777777777777779, 3.1415926809250987)
(10.0, 3.1415926809250987)
(10.0, 3.1415926809250987)