Sr Examen
Ecuación diferencial (y+cos(x)+2*x*y^2)dx+((2^y)*ln(2)+x+2*(x^2)*y)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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d 2 y(x) d 2 d x*--(y(x)) + 2*x*y (x) + 2 *--(y(x))*log(2) + 2*x *--(y(x))*y(x) + cos(x) + y(x) = 0 dx dx dx
$$2^{y{\left(x \right)}} \log{\left(2 \right)} \frac{d}{d x} y{\left(x \right)} + 2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 x y^{2}{\left(x \right)} + x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} + \cos{\left(x \right)} = 0$$
2^y*log(2)*y' + 2*x^2*y*y' + 2*x*y^2 + x*y' + y + cos(x) = 0
Respuesta
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y(x) 2 2 2 + x*y(x) + x *y (x) + sin(x) = C1
$$2^{y{\left(x \right)}} + x^{2} y^{2}{\left(x \right)} + x y{\left(x \right)} + \sin{\left(x \right)} = C_{1}$$
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, 0.9757497963690049)
(-5.555555555555555, 1.3375126999734002)
(-3.333333333333333, 2.194782392016796)
(-1.1111111111111107, 4.829823218009345)
(1.1111111111111107, 4.4066556317313506)
(3.333333333333334, 1.9204556938495911)
(5.555555555555557, 1.178051324186322)
(7.777777777777779, 0.8306512140366206)
(10.0, 0.6584592322065257)
(10.0, 0.6584592322065257)