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dx*(e^(y*x)*y*cos(2*x)-2*e^(y*x)*sin(2*x)+2*x)+dy*(e^(x*y)*x*cos(2*x)-3)=0
Ecuación diferencial dx*(e^(y*x)*y*cos(2*x)-2*e^(y*x)*sin(2*x)+2*x)+dy*(e^(x*y)*x*cos(2*x)-3)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d y*x(y) d y*x(y) d y*x(y)
-3 + 2*--(x(y))*x(y) + cos(2*x(y))*e *x(y) - 2*--(x(y))*e *sin(2*x(y)) + y*--(x(y))*cos(2*x(y))*e = 0
dy dy dy
$$y e^{y x{\left(y \right)}} \cos{\left(2 x{\left(y \right)} \right)} \frac{d}{d y} x{\left(y \right)} + x{\left(y \right)} e^{y x{\left(y \right)}} \cos{\left(2 x{\left(y \right)} \right)} + 2 x{\left(y \right)} \frac{d}{d y} x{\left(y \right)} - 2 e^{y x{\left(y \right)}} \sin{\left(2 x{\left(y \right)} \right)} \frac{d}{d y} x{\left(y \right)} - 3 = 0$$
y*exp(y*x)*cos(2*x)*x' + x*exp(y*x)*cos(2*x) + 2*x*x' - 2*exp(y*x)*sin(2*x)*x' - 3 = 0
Respuesta
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2 y*x(y) x (y) - 3*y + cos(2*x(y))*e = C1
$$- 3 y + x^{2}{\left(y \right)} + e^{y x{\left(y \right)}} \cos{\left(2 x{\left(y \right)} \right)} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
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(y, x):
(-10.0, 0.75)
(-7.777777777777778, 2.688718288003312)
(-5.555555555555555, 3.727716876795137)
(-3.333333333333333, 4.534593741624732)
(-1.1111111111111107, 5.218315616393013)
(1.1111111111111107, 5.501800619993813)
(3.333333333333334, 5.4977872028128045)
(5.555555555555557, 5.497787143316054)
(7.777777777777779, 5.497787143508194)
(10.0, 5.497787143700335)
(10.0, 5.497787143700335)