Sr Examen
Ecuación diferencial y''''+4y''=4e^(2x)*sin(x)-3e^(2x)*cos(x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 4
d d 2*x 2*x
4*---(y(x)) + ---(y(x)) = - 3*cos(x)*e + 4*e *sin(x)
2 4
dx dx
$$4 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{4}}{d x^{4}} y{\left(x \right)} = 4 e^{2 x} \sin{\left(x \right)} - 3 e^{2 x} \cos{\left(x \right)}$$
4*y'' + y'''' = 4*exp(2*x)*sin(x) - 3*exp(2*x)*cos(x)
Respuesta
[src]
2*x 2*x
7*cos(x)*e 4*e *sin(x)
y(x) = C1 + C2*x + C3*sin(2*x) + C4*cos(2*x) - ------------- - -------------
65 65
$$y{\left(x \right)} = C_{1} + C_{2} x + C_{3} \sin{\left(2 x \right)} + C_{4} \cos{\left(2 x \right)} - \frac{4 e^{2 x} \sin{\left(x \right)}}{65} - \frac{7 e^{2 x} \cos{\left(x \right)}}{65}$$
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