Sr Examen
Ecuación diferencial (d^2y/dx^2)-6*(dy/dx)+9*y=2*sin(2*x)+(1-x)*cos(3*x)
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Solución
Ha introducido
[src]
2
d d
- 6*--(y(x)) + 9*y(x) + ---(y(x)) = 2*sin(2*x) + (1 - x)*cos(3*x)
dx 2
dx
$$9 y{\left(x \right)} - 6 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = \left(1 - x\right) \cos{\left(3 x \right)} + 2 \sin{\left(2 x \right)}$$
9*y - 6*y' + y'' = (1 - x)*cos(3*x) + 2*sin(2*x)
Respuesta
[src]
sin(3*x) cos(3*x) 10*sin(2*x) 24*cos(2*x) 3*x x*sin(3*x)
y(x) = - -------- + -------- + ----------- + ----------- + (C1 + C2*x)*e + ----------
27 54 169 169 18
$$y{\left(x \right)} = \frac{x \sin{\left(3 x \right)}}{18} + \left(C_{1} + C_{2} x\right) e^{3 x} + \frac{10 \sin{\left(2 x \right)}}{169} - \frac{\sin{\left(3 x \right)}}{27} + \frac{24 \cos{\left(2 x \right)}}{169} + \frac{\cos{\left(3 x \right)}}{54}$$
Clasificación
nth linear constant coeff undetermined coefficients
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nth linear constant coeff variation of parameters Integral