Sr Examen
Ecuación diferencial dy^4/(dx^4)-9*dy^3/(dx^3)+30*dy^2/(dx^2)-44*dy/(dx)+24*y=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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3 2 4
d d d d
- 44*--(y(x)) - 9*---(y(x)) + 24*y(x) + 30*---(y(x)) + ---(y(x)) = 0
dx 3 2 4
dx dx dx
$$24 y{\left(x \right)} - 44 \frac{d}{d x} y{\left(x \right)} + 30 \frac{d^{2}}{d x^{2}} y{\left(x \right)} - 9 \frac{d^{3}}{d x^{3}} y{\left(x \right)} + \frac{d^{4}}{d x^{4}} y{\left(x \right)} = 0$$
24*y - 44*y' + 30*y'' - 9*y''' + y'''' = 0
Respuesta
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/ x \ 2*x y(x) = \C1 + C4*e + x*(C2 + C3*x)/*e
$$y{\left(x \right)} = \left(C_{1} + C_{4} e^{x} + x \left(C_{2} + C_{3} x\right)\right) e^{2 x}$$
Clasificación
nth linear constant coeff homogeneous