Sr Examen
Ecuación diferencial y''-25*y'=25*(sin(5*x)+cos(5*x))-50*e^(5*x)
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Solución
Ha introducido
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2
d d 5*x
- 25*--(y(x)) + ---(y(x)) = - 50*e + 25*cos(5*x) + 25*sin(5*x)
dx 2
dx
$$- 25 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = - 50 e^{5 x} + 25 \sin{\left(5 x \right)} + 25 \cos{\left(5 x \right)}$$
-25*y' + y'' = -50*exp(5*x) + 25*sin(5*x) + 25*cos(5*x)
Respuesta
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5*x
e 3*sin(5*x) 2*cos(5*x) 25*x
y(x) = C1 + ---- - ---------- + ---------- + C2*e
2 13 13
$$y{\left(x \right)} = C_{1} + C_{2} e^{25 x} + \frac{e^{5 x}}{2} - \frac{3 \sin{\left(5 x \right)}}{13} + \frac{2 \cos{\left(5 x \right)}}{13}$$
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