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Ecuación diferencial dx/dx=sec^2y/1+x^2

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v

Para el problema de Cauchy:

y() =
y'() =
y''() =
y'''() =
y''''() =

Gráfico:

interior superior

Solución

Ha introducido [src]
     2      2      
1 = x  + sec (y(x))
$$1 = x^{2} + \sec^{2}{\left(y{\left(x \right)} \right)}$$
1 = x^2 + sec(y)^2
Respuesta [src]
             / /       ____\ \
             | |      /  2 | |
             |-\1 + \/  x  / |
y(x) = -I*log|---------------|
             |     ________  |
             |    /      2   |
             \  \/  1 - x    /
$$y{\left(x \right)} = - i \log{\left(- \frac{\sqrt{x^{2}} + 1}{\sqrt{1 - x^{2}}} \right)}$$
             /        ____\
             |       /  2 |
             |-1 + \/  x  |
y(x) = -I*log|------------|
             |   ________ |
             |  /      2  |
             \\/  1 - x   /
$$y{\left(x \right)} = - i \log{\left(\frac{\sqrt{x^{2}} - 1}{\sqrt{1 - x^{2}}} \right)}$$
             / /        ____\ \
             | |       /  2 | |
             |-\-1 + \/  x  / |
y(x) = -I*log|----------------|
             |     ________   |
             |    /      2    |
             \  \/  1 - x     /
$$y{\left(x \right)} = - i \log{\left(- \frac{\sqrt{x^{2}} - 1}{\sqrt{1 - x^{2}}} \right)}$$
             /       ____\
             |      /  2 |
             |1 + \/  x  |
y(x) = -I*log|-----------|
             |   ________|
             |  /      2 |
             \\/  1 - x  /
$$y{\left(x \right)} = - i \log{\left(\frac{\sqrt{x^{2}} + 1}{\sqrt{1 - x^{2}}} \right)}$$
Clasificación
nth algebraic
nth algebraic Integral