Sr Examen

Ecuación diferencial y''-4*y'+13*y=26x+5

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Para el problema de Cauchy:

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

Gráfico:

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Solución

Ha introducido [src]
                           2                 
    d                     d                  
- 4*--(y(x)) + 13*y(x) + ---(y(x)) = 5 + 26*x
    dx                     2                 
                         dx                  
$$13 y{\left(x \right)} - 4 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 26 x + 5$$
13*y - 4*y' + y'' = 26*x + 5
Respuesta [src]
                                              2*x
y(x) = 1 + 2*x + (C1*sin(3*x) + C2*cos(3*x))*e   
$$y{\left(x \right)} = 2 x + \left(C_{1} \sin{\left(3 x \right)} + C_{2} \cos{\left(3 x \right)}\right) e^{2 x} + 1$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral