Sr Examen
Ecuación diferencial 4*y'-5*y''+y'''=-e^2*x^2*sin(x)+3*e^(3*x)+4*x
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Solución
Ha introducido
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2 3
d d d 3*x 2 2
- 5*---(y(x)) + 4*--(y(x)) + ---(y(x)) = 3*e + 4*x - x *e *sin(x)
2 dx 3
dx dx
$$4 \frac{d}{d x} y{\left(x \right)} - 5 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = - x^{2} e^{2} \sin{\left(x \right)} + 4 x + 3 e^{3 x}$$
4*y' - 5*y'' + y''' = -x^2*exp(2)*sin(x) + 4*x + 3*exp(3*x)
Respuesta
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2 3*x 2 2 2 2 2 2 2 2
x e 5*x x 4*x 6535*cos(x)*e 1655*e *sin(x) 142*x*e *sin(x) 95*x*cos(x)*e 5*x *e *sin(x) 3*x *cos(x)*e
y(x) = C1 + -- - ---- + --- + C2*e + C3*e - -------------- + -------------- - --------------- - -------------- - -------------- + --------------
2 2 4 9826 9826 289 289 34 34
$$y{\left(x \right)} = C_{1} + C_{2} e^{x} + C_{3} e^{4 x} - \frac{5 x^{2} e^{2} \sin{\left(x \right)}}{34} + \frac{3 x^{2} e^{2} \cos{\left(x \right)}}{34} + \frac{x^{2}}{2} - \frac{142 x e^{2} \sin{\left(x \right)}}{289} - \frac{95 x e^{2} \cos{\left(x \right)}}{289} + \frac{5 x}{4} - \frac{e^{3 x}}{2} + \frac{1655 e^{2} \sin{\left(x \right)}}{9826} - \frac{6535 e^{2} \cos{\left(x \right)}}{9826}$$
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