Sr Examen
Ecuación diferencial ((x)^4lnx-2xy^3)dx+3x^2y^2dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
4 3 2 2 d
x *log(x) - 2*x*y (x) + 3*x *y (x)*--(y(x)) = 0
dx
$$x^{4} \log{\left(x \right)} + 3 x^{2} y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 2 x y^{3}{\left(x \right)} = 0$$
x^4*log(x) + 3*x^2*y^2*y' - 2*x*y^3 = 0
Respuesta
[src]
________________________
3 / 2 / ___\
\/ x *(C1 + x - x*log(x)) *\-1 - I*\/ 3 /
y(x) = ------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{x^{2} \left(C_{1} - x \log{\left(x \right)} + x\right)} \left(-1 - \sqrt{3} i\right)}{2}$$
________________________
3 / 2 / ___\
\/ x *(C1 + x - x*log(x)) *\-1 + I*\/ 3 /
y(x) = ------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{x^{2} \left(C_{1} - x \log{\left(x \right)} + x\right)} \left(-1 + \sqrt{3} i\right)}{2}$$
________________________
3 / 2
y(x) = \/ x *(C1 + x - x*log(x))
$$y{\left(x \right)} = \sqrt[3]{x^{2} \left(C_{1} - x \log{\left(x \right)} + x\right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
almost linear
lie group
1st exact Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, nan)
(-5.555555555555555, nan)
(-3.333333333333333, nan)
(-1.1111111111111107, nan)
(1.1111111111111107, nan)
(3.333333333333334, nan)
(5.555555555555557, nan)
(7.777777777777779, nan)
(10.0, nan)
(10.0, nan)