Sr Examen
Ecuación diferencial y''-2*y'+5y=3*e^(2*x)+2*e^x-16*sin(2*x)+5x^2
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Solución
Ha introducido
[src]
2
d d x 2*x 2
- 2*--(y(x)) + 5*y(x) + ---(y(x)) = -16*sin(2*x) + 2*e + 3*e + 5*x
dx 2
dx
$$5 y{\left(x \right)} - 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 5 x^{2} + 3 e^{2 x} + 2 e^{x} - 16 \sin{\left(2 x \right)}$$
5*y - 2*y' + y'' = 5*x^2 + 3*exp(2*x) + 2*exp(x) - 16*sin(2*x)
Respuesta
[src]
2*x
2 2 64*cos(2*x) 16*sin(2*x) 3*e 4*x x
y(x) = - -- + x - ----------- - ----------- + ------ + --- + (1/2 + C1*sin(2*x) + C2*cos(2*x))*e
25 17 17 5 5
$$y{\left(x \right)} = x^{2} + \frac{4 x}{5} + \left(C_{1} \sin{\left(2 x \right)} + C_{2} \cos{\left(2 x \right)} + \frac{1}{2}\right) e^{x} + \frac{3 e^{2 x}}{5} - \frac{16 \sin{\left(2 x \right)}}{17} - \frac{64 \cos{\left(2 x \right)}}{17} - \frac{2}{25}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral