Sr Examen
Ecuación diferencial y''-6y'+25y=(32x-12)*sin(x)-36x*cos(3x)
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Solución
Ha introducido
[src]
2
d d
- 6*--(y(x)) + 25*y(x) + ---(y(x)) = (-12 + 32*x)*sin(x) - 36*x*cos(3*x)
dx 2
dx
$$25 y{\left(x \right)} - 6 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = - 36 x \cos{\left(3 x \right)} + \left(32 x - 12\right) \sin{\left(x \right)}$$
25*y - 6*y' + y'' = -36*x*cos(3*x) + (32*x - 12)*sin(x)
Respuesta
[src]
6858*cos(3*x) 376*sin(x) 18*cos(x) 8694*sin(3*x) 3*x 144*x*cos(3*x) 16*x*cos(x) 64*x*sin(x) 162*x*sin(3*x)
y(x) = - ------------- - ---------- - --------- + ------------- + (C1*sin(4*x) + C2*cos(4*x))*e - -------------- + ----------- + ----------- + --------------
21025 2601 289 21025 145 51 51 145
$$y{\left(x \right)} = \frac{64 x \sin{\left(x \right)}}{51} + \frac{162 x \sin{\left(3 x \right)}}{145} + \frac{16 x \cos{\left(x \right)}}{51} - \frac{144 x \cos{\left(3 x \right)}}{145} + \left(C_{1} \sin{\left(4 x \right)} + C_{2} \cos{\left(4 x \right)}\right) e^{3 x} - \frac{376 \sin{\left(x \right)}}{2601} + \frac{8694 \sin{\left(3 x \right)}}{21025} - \frac{18 \cos{\left(x \right)}}{289} - \frac{6858 \cos{\left(3 x \right)}}{21025}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral