Sr Examen
Ecuación diferencial y''''+5*y''+4*y=sin(x)*cos(2x)
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Solución
Ha introducido
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2 4
d d
4*y(x) + 5*---(y(x)) + ---(y(x)) = cos(2*x)*sin(x)
2 4
dx dx
$$4 y{\left(x \right)} + 5 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{4}}{d x^{4}} y{\left(x \right)} = \sin{\left(x \right)} \cos{\left(2 x \right)}$$
4*y + 5*y'' + y'''' = sin(x)*cos(2*x)
Respuesta
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/ 3 2\
sin(7*x) sin(5*x) 13*sin(3*x) / x \ | (1 - cos(2*x)) 4*(1 - cos(2*x)) |
y(x) = - -------- + -------- + ----------- + C3*sin(2*x) + C4*cos(2*x) + |C1 + --|*cos(x) + |C2 - --------------- + -----------------|*sin(x)
240 144 360 \ 12/ \ 30 45 /
$$y{\left(x \right)} = C_{3} \sin{\left(2 x \right)} + C_{4} \cos{\left(2 x \right)} + \left(C_{1} + \frac{x}{12}\right) \cos{\left(x \right)} + \left(C_{2} - \frac{\left(1 - \cos{\left(2 x \right)}\right)^{3}}{30} + \frac{4 \left(1 - \cos{\left(2 x \right)}\right)^{2}}{45}\right) \sin{\left(x \right)} + \frac{13 \sin{\left(3 x \right)}}{360} + \frac{\sin{\left(5 x \right)}}{144} - \frac{\sin{\left(7 x \right)}}{240}$$
Clasificación
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral