Sr Examen
Ecuación diferencial y''+3*y'+4y=x^2-7*sin(x)
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Solución
Ha introducido
[src]
2
d d 2
3*--(y(x)) + 4*y(x) + ---(y(x)) = x - 7*sin(x)
dx 2
dx
$$4 y{\left(x \right)} + 3 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = x^{2} - 7 \sin{\left(x \right)}$$
4*y + 3*y' + y'' = x^2 - 7*sin(x)
Respuesta
[src]
-3*x
2 / / ___\ / ___\\ ----
5 7*sin(x) 3*x x 7*cos(x) | |x*\/ 7 | |x*\/ 7 || 2
y(x) = -- - -------- - --- + -- + -------- + |C1*sin|-------| + C2*cos|-------||*e
32 6 8 4 6 \ \ 2 / \ 2 //
$$y{\left(x \right)} = \frac{x^{2}}{4} - \frac{3 x}{8} + \left(C_{1} \sin{\left(\frac{\sqrt{7} x}{2} \right)} + C_{2} \cos{\left(\frac{\sqrt{7} x}{2} \right)}\right) e^{- \frac{3 x}{2}} - \frac{7 \sin{\left(x \right)}}{6} + \frac{7 \cos{\left(x \right)}}{6} + \frac{5}{32}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral