Sr Examen
Ecuación diferencial y'''+6y''+9y'=5x-(x^2+1)*e^(2x)*sin3x+2e^(2x)
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Solución
Ha introducido
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2 3
d d d 2*x / 2\ 2*x
6*---(y(x)) + 9*--(y(x)) + ---(y(x)) = 2*e + 5*x - \1 + x /*e *sin(3*x)
2 dx 3
dx dx
$$9 \frac{d}{d x} y{\left(x \right)} + 6 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 5 x - \left(x^{2} + 1\right) e^{2 x} \sin{\left(3 x \right)} + 2 e^{2 x}$$
9*y' + 6*y'' + y''' = 5*x - (x^2 + 1)*exp(2*x)*sin(3*x) + 2*exp(2*x)
Respuesta
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2*x 2 2*x 2*x 2*x 2*x 2 2*x 2 2*x
10*x e 5*x -3*x 2033379*cos(3*x)*e 2749463*e *sin(3*x) 7731*x*e *sin(3*x) 2736*x*cos(3*x)*e 27*x *cos(3*x)*e 29*x *e *sin(3*x)
y(x) = C1 - ---- + ---- + ---- + (C2 + C3*x)*e + --------------------- + --------------------- - -------------------- - -------------------- + ------------------- + -------------------
27 25 18 366991274 366991274 830297 830297 3757 7514
$$y{\left(x \right)} = C_{1} + \frac{29 x^{2} e^{2 x} \sin{\left(3 x \right)}}{7514} + \frac{27 x^{2} e^{2 x} \cos{\left(3 x \right)}}{3757} + \frac{5 x^{2}}{18} - \frac{7731 x e^{2 x} \sin{\left(3 x \right)}}{830297} - \frac{2736 x e^{2 x} \cos{\left(3 x \right)}}{830297} - \frac{10 x}{27} + \left(C_{2} + C_{3} x\right) e^{- 3 x} + \frac{2749463 e^{2 x} \sin{\left(3 x \right)}}{366991274} + \frac{2033379 e^{2 x} \cos{\left(3 x \right)}}{366991274} + \frac{e^{2 x}}{25}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral