Sr Examen
Ecuación diferencial y'''-4y''+13y'=-xe^(2x)cos(3x)-xsin(3x)-e
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Solución
Ha introducido
[src]
2 3
d d d 2*x
- 4*---(y(x)) + 13*--(y(x)) + ---(y(x)) = -E - x*sin(3*x) - x*cos(3*x)*e
2 dx 3
dx dx
$$13 \frac{d}{d x} y{\left(x \right)} - 4 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = - x e^{2 x} \cos{\left(3 x \right)} - x \sin{\left(3 x \right)} - e$$
13*y' - 4*y'' + y''' = -x*exp(2*x)*cos(3*x) - x*sin(3*x) - E
Respuesta
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// 2\ / 2\ \
4*sin(3*x) 3*cos(3*x) || 23*x x | | 49*x x | | 2*x E*x x*sin(3*x) x*cos(3*x)
y(x) = C1 - ---------- - ---------- + ||C2 - ---- - --|*sin(3*x) + |C3 - ---- + --|*cos(3*x)|*e - --- - ---------- + ----------
225 400 \\ 2028 78/ \ 3042 52/ / 13 40 120
$$y{\left(x \right)} = C_{1} - \frac{x \sin{\left(3 x \right)}}{40} + \frac{x \cos{\left(3 x \right)}}{120} - \frac{e x}{13} + \left(\left(C_{2} - \frac{x^{2}}{78} - \frac{23 x}{2028}\right) \sin{\left(3 x \right)} + \left(C_{3} + \frac{x^{2}}{52} - \frac{49 x}{3042}\right) \cos{\left(3 x \right)}\right) e^{2 x} - \frac{4 \sin{\left(3 x \right)}}{225} - \frac{3 \cos{\left(3 x \right)}}{400}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral