Sr Examen
Ecuación diferencial y'''-6y''+9y'=2-x+x*(e^(3x))*sin(3x)-4*(e^(3x))
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 3
d d d 3*x 3*x
- 6*---(y(x)) + 9*--(y(x)) + ---(y(x)) = 2 - x - 4*e + x*e *sin(3*x)
2 dx 3
dx dx
$$9 \frac{d}{d x} y{\left(x \right)} - 6 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = x e^{3 x} \sin{\left(3 x \right)} - x - 4 e^{3 x} + 2$$
9*y' - 6*y'' + y''' = x*exp(3*x)*sin(3*x) - x - 4*exp(3*x) + 2
Respuesta
[src]
2
x 4*x / cos(3*x) sin(3*x) / 2*x sin(3*x) cos(3*x)\\ 3*x
y(x) = C1 - -- + --- + |C2 - -------- - -------- + x*|C3 - --- - -------- + --------||*e
18 27 \ 54 81 \ 3 54 54 //
$$y{\left(x \right)} = C_{1} - \frac{x^{2}}{18} + \frac{4 x}{27} + \left(C_{2} + x \left(C_{3} - \frac{2 x}{3} - \frac{\sin{\left(3 x \right)}}{54} + \frac{\cos{\left(3 x \right)}}{54}\right) - \frac{\sin{\left(3 x \right)}}{81} - \frac{\cos{\left(3 x \right)}}{54}\right) e^{3 x}$$
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