Sr Examen
Ecuación diferencial y''+2y'+4y=5x⁴+3x²-x
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Solución
Ha introducido
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2
d d 2 4
2*--(y(x)) + 4*y(x) + ---(y(x)) = -x + 3*x + 5*x
dx 2
dx
$$4 y{\left(x \right)} + 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 5 x^{4} + 3 x^{2} - x$$
4*y + 2*y' + y'' = 5*x^4 + 3*x^2 - x
Respuesta
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3 2 4
7 5*x 3*x 5*x 11*x / / ___\ / ___\\ -x
y(x) = - - - ---- + ---- + ---- + ---- + \C1*sin\x*\/ 3 / + C2*cos\x*\/ 3 //*e
4 2 4 4 4
$$y{\left(x \right)} = \frac{5 x^{4}}{4} - \frac{5 x^{3}}{2} + \frac{3 x^{2}}{4} + \frac{11 x}{4} + \left(C_{1} \sin{\left(\sqrt{3} x \right)} + C_{2} \cos{\left(\sqrt{3} x \right)}\right) e^{- x} - \frac{7}{4}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral