Sr Examen
Ecuación diferencial (x^2-y^2)dy/dx=2xy
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Solución
Ha introducido
[src]
/ 2 2 \ d
\x - y (x)/*--(y(x)) = 2*x*y(x)
dx
$$\left(x^{2} - y^{2}{\left(x \right)}\right) \frac{d}{d x} y{\left(x \right)} = 2 x y{\left(x \right)}$$
(x^2 - y^2)*y' = 2*x*y
Respuesta
[src]
____________
/ 2 2
C1 \/ C1 - 4*x
y(x) = - -- - ---------------
2 2
$$y{\left(x \right)} = - \frac{C_{1}}{2} - \frac{\sqrt{C_{1}^{2} - 4 x^{2}}}{2}$$
____________
/ 2 2
\/ C1 - 4*x C1
y(x) = --------------- - --
2 2
$$y{\left(x \right)} = - \frac{C_{1}}{2} + \frac{\sqrt{C_{1}^{2} - 4 x^{2}}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st homogeneous coeff best
1st homogeneous coeff subs indep div dep
1st homogeneous coeff subs dep div indep
1st power series
lie group
1st exact Integral
1st homogeneous coeff subs indep div dep Integral
1st homogeneous coeff subs dep div indep Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.4526943224573934)
(-5.555555555555555, 0.23058322858717029)
(-3.333333333333333, 0.08291849032780002)
(-1.1111111111111107, 0.009208103638242515)
(1.1111111111111107, 0.009208297030665039)
(3.333333333333334, 0.08292054506602224)
(5.555555555555557, 0.23058895983079522)
(7.777777777777779, 0.45270561751382554)
(10.0, 0.7500188730281889)
(10.0, 0.7500188730281889)