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Ecuación diferencial y"'+y'=tanx

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Para el problema de Cauchy:

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

Gráfico:

interior superior

Solución

Ha introducido [src]
             3               
d           d                
--(y(x)) + ---(y(x)) = tan(x)
dx           3               
           dx                
$$\frac{d}{d x} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = \tan{\left(x \right)}$$
y' + y''' = tan(x)
Respuesta [src]
                                      /     log(-1 + sin(x))   log(1 + sin(x))\       
y(x) = C1 - log(cos(x)) + C3*cos(x) + |C2 + ---------------- - ---------------|*sin(x)
                                      \            2                  2       /       
$$y{\left(x \right)} = C_{1} + C_{3} \cos{\left(x \right)} + \left(C_{2} + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}\right) \sin{\left(x \right)} - \log{\left(\cos{\left(x \right)} \right)}$$
Clasificación
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral