Sr Examen
Ecuación diferencial y''+4y'+3y=excos2x-cos3x-3x^3
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Solución
Ha introducido
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2
d d 3 x
3*y(x) + 4*--(y(x)) + ---(y(x)) = -cos(3*x) - 3*x + cos(2*x)*e
dx 2
dx
$$3 y{\left(x \right)} + 4 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = - 3 x^{3} + e^{x} \cos{\left(2 x \right)} - \cos{\left(3 x \right)}$$
3*y + 4*y' + y'' = -3*x^3 + exp(x)*cos(2*x) - cos(3*x)
Respuesta
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x
80 3 2 26*x sin(3*x) cos(3*x) -3*x -x (3*sin(2*x) + cos(2*x))*e
y(x) = -- - x + 4*x - ---- - -------- + -------- + C1*e + C2*e + --------------------------
9 3 15 30 40
$$y{\left(x \right)} = C_{1} e^{- 3 x} + C_{2} e^{- x} - x^{3} + 4 x^{2} - \frac{26 x}{3} + \frac{\left(3 \sin{\left(2 x \right)} + \cos{\left(2 x \right)}\right) e^{x}}{40} - \frac{\sin{\left(3 x \right)}}{15} + \frac{\cos{\left(3 x \right)}}{30} + \frac{80}{9}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral