Sr Examen
Ecuación diferencial y'''-13*y''+12y'=3*x^2-2x+1
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Solución
Ha introducido
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2 3
d d d 2
- 13*---(y(x)) + 12*--(y(x)) + ---(y(x)) = 1 - 2*x + 3*x
2 dx 3
dx dx
$$12 \frac{d}{d x} y{\left(x \right)} - 13 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 3 x^{2} - 2 x + 1$$
12*y' - 13*y'' + y''' = 3*x^2 - 2*x + 1
Respuesta
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3 2
x 3*x 43*x x 12*x
y(x) = C1 + -- + ---- + ---- + C2*e + C3*e
12 16 96
$$y{\left(x \right)} = C_{1} + C_{2} e^{x} + C_{3} e^{12 x} + \frac{x^{3}}{12} + \frac{3 x^{2}}{16} + \frac{43 x}{96}$$
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