Sr Examen
Ecuación diferencial y''-4y'+4y=sen(3x)*e^2x
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Solución
Ha introducido
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2
d d 2
- 4*--(y(x)) + 4*y(x) + ---(y(x)) = x*e *sin(3*x)
dx 2
dx
$$4 y{\left(x \right)} - 4 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = x e^{2} \sin{\left(3 x \right)}$$
4*y - 4*y' + y'' = x*exp(2)*sin(3*x)
Respuesta
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2 2 2 2
2*x 92*e *sin(3*x) 18*cos(3*x)*e 5*x*e *sin(3*x) 12*x*cos(3*x)*e
y(x) = (C1 + C2*x)*e - -------------- + -------------- - --------------- + ----------------
2197 2197 169 169
$$y{\left(x \right)} = - \frac{5 x e^{2} \sin{\left(3 x \right)}}{169} + \frac{12 x e^{2} \cos{\left(3 x \right)}}{169} + \left(C_{1} + C_{2} x\right) e^{2 x} - \frac{92 e^{2} \sin{\left(3 x \right)}}{2197} + \frac{18 e^{2} \cos{\left(3 x \right)}}{2197}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral