Sr Examen
Ecuación diferencial y’’-2y’+y=(xe^2x)sin2x
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Solución
Ha introducido
[src]
2
d d 2 2
- 2*--(y(x)) + ---(y(x)) + y(x) = x *e *sin(2*x)
dx 2
dx
$$y{\left(x \right)} - 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = x^{2} e^{2} \sin{\left(2 x \right)}$$
y - 2*y' + y'' = x^2*exp(2)*sin(2*x)
Respuesta
[src]
2 2 2 2 2 2 2 2
x 144*cos(2*x)*e 42*e *sin(2*x) 44*x*e *sin(2*x) 8*x*cos(2*x)*e 3*x *e *sin(2*x) 4*x *cos(2*x)*e
y(x) = (C1 + C2*x)*e - --------------- - -------------- - ---------------- - --------------- - ---------------- + ----------------
625 625 125 125 25 25
$$y{\left(x \right)} = - \frac{3 x^{2} e^{2} \sin{\left(2 x \right)}}{25} + \frac{4 x^{2} e^{2} \cos{\left(2 x \right)}}{25} - \frac{44 x e^{2} \sin{\left(2 x \right)}}{125} - \frac{8 x e^{2} \cos{\left(2 x \right)}}{125} + \left(C_{1} + C_{2} x\right) e^{x} - \frac{42 e^{2} \sin{\left(2 x \right)}}{625} - \frac{144 e^{2} \cos{\left(2 x \right)}}{625}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral