Sr Examen
Ecuación diferencial y"+4*y'+5*y=(e^(-2x))*(1+sec(x)^2)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2
d d / 2 \ -2*x
4*--(y(x)) + 5*y(x) + ---(y(x)) = \1 + sec (x)/*e
dx 2
dx
$$5 y{\left(x \right)} + 4 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = \left(\sec^{2}{\left(x \right)} + 1\right) e^{- 2 x}$$
5*y + 4*y' + y'' = (sec(x)^2 + 1)*exp(-2*x)
Respuesta
[src]
/ / log(1 + sin(x)) log(-1 + sin(x))\ \ -2*x
y(x) = |C2*cos(x) + |C1 + --------------- - ----------------|*sin(x)|*e
\ \ 2 2 / /
$$y{\left(x \right)} = \left(C_{2} \cos{\left(x \right)} + \left(C_{1} - \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}\right) \sin{\left(x \right)}\right) e^{- 2 x}$$
Clasificación
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral