Sr Examen
Ecuación diferencial (2*x*y^2-3*y)dx+(2*y*x^2-3*x+1)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 2 d d
-3*y(x) - 3*x*--(y(x)) + 2*x*y (x) + 2*x *--(y(x))*y(x) + --(y(x)) = 0
dx dx dx
$$2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 x y^{2}{\left(x \right)} - 3 x \frac{d}{d x} y{\left(x \right)} - 3 y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$
2*x^2*y*y' + 2*x*y^2 - 3*x*y' - 3*y + y' = 0
Respuesta
[src]
________________________
/ 2 2
1 \/ 1 - 6*x + 9*x + C1*x
3 - - - ---------------------------
x x
y(x) = -----------------------------------
2*x
$$y{\left(x \right)} = \frac{3 - \frac{\sqrt{C_{1} x^{2} + 9 x^{2} - 6 x + 1}}{x} - \frac{1}{x}}{2 x}$$
________________________
/ 2 2
1 \/ 1 - 6*x + 9*x + C1*x
3 - - + ---------------------------
x x
y(x) = -----------------------------------
2*x
$$y{\left(x \right)} = \frac{3 + \frac{\sqrt{C_{1} x^{2} + 9 x^{2} - 6 x + 1}}{x} - \frac{1}{x}}{2 x}$$
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, 0.9627650267335662)
(-5.555555555555555, 1.344048774493064)
(-3.333333333333333, 2.2252993785518154)
(-1.1111111111111107, 6.459322273472587)
(1.1111111111111107, 9.025106852581505)
(3.333333333333334, 3.1103718826718847)
(5.555555555555557, 1.8786750425478105)
(7.777777777777779, 1.345737886998647)
(10.0, 1.0483418161379483)
(10.0, 1.0483418161379483)