Sr Examen
Ecuación diferencial 9*y-6*y'+y''=e^3*x+3*x^2+8*e^(-3*x)*x*cos(x)
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Solución
Ha introducido
[src]
2
d d 2 3 -3*x
- 6*--(y(x)) + 9*y(x) + ---(y(x)) = 3*x + x*e + 8*x*cos(x)*e
dx 2
dx
$$9 y{\left(x \right)} - 6 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 3 x^{2} + x e^{3} + 8 x e^{- 3 x} \cos{\left(x \right)}$$
9*y - 6*y' + y'' = 3*x^2 + x*exp(3) + 8*x*exp(-3*x)*cos(x)
Respuesta
[src]
2 3 3 -3*x
2 x 2*e 4*x 3*x x*e 8*(-214*sin(x) + 396*cos(x) - 444*x*sin(x) + 1295*x*cos(x))*e
y(x) = - + -- + ---- + --- + (C1 + C2*x)*e + ---- + -----------------------------------------------------------------
9 3 27 9 9 50653
$$y{\left(x \right)} = \frac{x^{2}}{3} + \frac{4 x}{9} + \frac{x e^{3}}{9} + \left(C_{1} + C_{2} x\right) e^{3 x} + \frac{8 \left(- 444 x \sin{\left(x \right)} + 1295 x \cos{\left(x \right)} - 214 \sin{\left(x \right)} + 396 \cos{\left(x \right)}\right) e^{- 3 x}}{50653} + \frac{2}{9} + \frac{2 e^{3}}{27}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral