Sr Examen
Ecuación diferencial dx*e^(y^2)*x+dy*(e^(y^2)*x^2*y+tan(y)^2)=0
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Solución
Ha introducido
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2 2
y (x) 2 d 2 d y (x)
x*e + tan (y(x))*--(y(x)) + x *--(y(x))*e *y(x) = 0
dx dx
$$x^{2} y{\left(x \right)} e^{y^{2}{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} + x e^{y^{2}{\left(x \right)}} + \tan^{2}{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y*exp(y^2)*y' + x*exp(y^2) + tan(y)^2*y' = 0
Respuesta
[src]
2
2 y (x)
sin(y(x)) x *e
-y(x) + --------- + --------- = C1
cos(y(x)) 2
$$\frac{x^{2} e^{y^{2}{\left(x \right)}}}{2} - y{\left(x \right)} + \frac{\sin{\left(y{\left(x \right)} \right)}}{\cos{\left(y{\left(x \right)} \right)}} = C_{1}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral