Sr Examen
Ecuación diferencial y'''+y''+3*y'-5*y=5*sin2x+10*x^2+3*x+7
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Solución
Ha introducido
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2 3
d d d 2
-5*y(x) + 3*--(y(x)) + ---(y(x)) + ---(y(x)) = 7 + 3*x + 5*sin(2*x) + 10*x
dx 2 3
dx dx
$$- 5 y{\left(x \right)} + 3 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 10 x^{2} + 3 x + 5 \sin{\left(2 x \right)} + 7$$
-5*y + 3*y' + y'' + y''' = 10*x^2 + 3*x + 5*sin(2*x) + 7
Respuesta
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2 9*sin(2*x) 2*cos(2*x) x -x
y(x) = -4 - 3*x - 2*x - ---------- + ---------- + C3*e + (C1*sin(2*x) + C2*cos(2*x))*e
17 17
$$y{\left(x \right)} = C_{3} e^{x} - 2 x^{2} - 3 x + \left(C_{1} \sin{\left(2 x \right)} + C_{2} \cos{\left(2 x \right)}\right) e^{- x} - \frac{9 \sin{\left(2 x \right)}}{17} + \frac{2 \cos{\left(2 x \right)}}{17} - 4$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral