Sr Examen
Ecuación diferencial y''+14y+65y=2x^2+x+e^(-7x)*(cos4x+2sin4x)
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Solución
Ha introducido
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2
d 2 -7*x
79*y(x) + ---(y(x)) = x + 2*x + (2*sin(4*x) + cos(4*x))*e
2
dx
$$79 y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 2 x^{2} + x + \left(2 \sin{\left(4 x \right)} + \cos{\left(4 x \right)}\right) e^{- 7 x}$$
79*y + y'' = 2*x^2 + x + (2*sin(4*x) + cos(4*x))*exp(-7*x)
Respuesta
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2 -7*x -7*x
4 x 2*x / ____\ / ____\ cos(4*x)*e 3*e *sin(4*x)
y(x) = - ---- + -- + ---- + C1*sin\x*\/ 79 / + C2*cos\x*\/ 79 / + -------------- + ----------------
6241 79 79 70 280
$$y{\left(x \right)} = C_{1} \sin{\left(\sqrt{79} x \right)} + C_{2} \cos{\left(\sqrt{79} x \right)} + \frac{2 x^{2}}{79} + \frac{x}{79} - \frac{4}{6241} + \frac{3 e^{- 7 x} \sin{\left(4 x \right)}}{280} + \frac{e^{- 7 x} \cos{\left(4 x \right)}}{70}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral