Sr Examen
Ecuación diferencial -y-y'+y''+y'''=e^x*x^4-2*x*sin(x)+cos(x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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2 3
d d d 4 x
- --(y(x)) - y(x) + ---(y(x)) + ---(y(x)) = x *e - 2*x*sin(x) + cos(x)
dx 2 3
dx dx
$$- y{\left(x \right)} - \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = x^{4} e^{x} - 2 x \sin{\left(x \right)} + \cos{\left(x \right)}$$
-y - y' + y'' + y''' = x^4*exp(x) - 2*x*sin(x) + cos(x)
Respuesta
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/ 2 4 5 3 \
sin(x) 3*cos(x) -x | 3*x x x 3*x 15*x| x x*sin(x) x*cos(x)
y(x) = ------ + -------- + (C1 + C2*x)*e + |C3 - ---- - -- + -- + ---- + ----|*e + -------- - --------
4 4 \ 2 4 20 4 8 / 2 2
$$y{\left(x \right)} = \frac{x \sin{\left(x \right)}}{2} - \frac{x \cos{\left(x \right)}}{2} + \left(C_{1} + C_{2} x\right) e^{- x} + \left(C_{3} + \frac{x^{5}}{20} - \frac{x^{4}}{4} + \frac{3 x^{3}}{4} - \frac{3 x^{2}}{2} + \frac{15 x}{8}\right) e^{x} + \frac{\sin{\left(x \right)}}{4} + \frac{3 \cos{\left(x \right)}}{4}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral