Sr Examen
Ecuación diferencial y''+2y'+2y=xe^(2x)cos(3x)+2e^(-x)sin(x)
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Solución
Ha introducido
[src]
2
d d -x 2*x
2*--(y(x)) + 2*y(x) + ---(y(x)) = 2*e *sin(x) + x*cos(3*x)*e
dx 2
dx
$$2 y{\left(x \right)} + 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = x e^{2 x} \cos{\left(3 x \right)} + 2 e^{- x} \sin{\left(x \right)}$$
2*y + 2*y' + y'' = x*exp(2*x)*cos(3*x) + 2*exp(-x)*sin(x)
Respuesta
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2*x
-x (-2154*sin(3*x) + 1722*cos(3*x) + 325*x*cos(3*x) + 5850*x*sin(3*x))*e
y(x) = (C2*sin(x) + (C1 - x)*cos(x))*e + ------------------------------------------------------------------------
105625
$$y{\left(x \right)} = \left(C_{2} \sin{\left(x \right)} + \left(C_{1} - x\right) \cos{\left(x \right)}\right) e^{- x} + \frac{\left(5850 x \sin{\left(3 x \right)} + 325 x \cos{\left(3 x \right)} - 2154 \sin{\left(3 x \right)} + 1722 \cos{\left(3 x \right)}\right) e^{2 x}}{105625}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral