Sr Examen
Ecuación diferencial y'''-2y''+2y'=5cosx+2x
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
- 2*---(y(x)) + 2*--(y(x)) + ---(y(x)) = 2*x + 5*cos(x)
2 dx 3
dx dx
$$2 \frac{d}{d x} y{\left(x \right)} - 2 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 2 x + 5 \cos{\left(x \right)}$$
2*y' - 2*y'' + y''' = 2*x + 5*cos(x)
Respuesta
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2
x x
y(x) = C1 + x + -- + 2*cos(x) + (C2*sin(x) + C3*cos(x))*e + sin(x)
2
$$y{\left(x \right)} = C_{1} + \frac{x^{2}}{2} + x + \left(C_{2} \sin{\left(x \right)} + C_{3} \cos{\left(x \right)}\right) e^{x} + \sin{\left(x \right)} + 2 \cos{\left(x \right)}$$