Sr Examen
Ecuación diferencial y’-3y/x=xy^4
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Solución
Ha introducido
[src]
3*y(x) d 4
- ------ + --(y(x)) = x*y (x)
x dx
$$\frac{d}{d x} y{\left(x \right)} - \frac{3 y{\left(x \right)}}{x} = x y^{4}{\left(x \right)}$$
y' - 3*y/x = x*y^4
Respuesta
[src]
____________
/ 9
3 ____ / -x
y(x) = \/ 11 * / ----------
3 / 11
\/ C1 + 3*x
$$y{\left(x \right)} = \sqrt[3]{11} \sqrt[3]{- \frac{x^{9}}{C_{1} + 3 x^{11}}}$$
____________
/ 9
3 ____ / -x / ___\
\/ 11 * / ---------- *\-1 - I*\/ 3 /
3 / 11
\/ C1 + 3*x
y(x) = ----------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{11} \sqrt[3]{- \frac{x^{9}}{C_{1} + 3 x^{11}}} \left(-1 - \sqrt{3} i\right)}{2}$$
____________
/ 9
3 ____ / -x / ___\
\/ 11 * / ---------- *\-1 + I*\/ 3 /
3 / 11
\/ C1 + 3*x
y(x) = ----------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{11} \sqrt[3]{- \frac{x^{9}}{C_{1} + 3 x^{11}}} \left(-1 + \sqrt{3} i\right)}{2}$$
Gráfico para el problema de Cauchy
Clasificación
Bernoulli
separable reduced
lie group
Bernoulli Integral
separable reduced Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.1550853084466426)
(-5.555555555555555, 0.05543046339458695)
(-3.333333333333333, 0.011967282134591068)
(-1.1111111111111107, 0.0004432319788134448)
(1.1111111111111107, -0.0004439750223292228)
(3.333333333333334, -0.01198648006037442)
(5.555555555555557, -0.05546626152277093)
(7.777777777777779, -0.14942540766885576)
(10.0, -0.26018608530429044)
(10.0, -0.26018608530429044)