10y^{''}+90y^'+1/(0.05)y=500sin(x)

Lösung

10 y^{^{''}} + 90 y^{^{'}} + \frac{1}{0.05} y = 500 sin (x)

y = c_{1} e^{\frac{( - 9 + 73 ) x}{2}} + c_{2} e^{- \frac{( 9 + 73 ) x}{2}} + \frac{25}{41} sin (x) - \frac{225}{41} cos (x)

Schritte zur Lösung

10 y^{''} (x) + 90 y^{'} (x) + \frac{1}{0.05} y = 500 sin (x)

Solve linear ODE:

y = c_{1} e^{\frac{( - 9 + 73 ) x}{2}} + c_{2} e^{- \frac{( 9 + 73 ) x}{2}} + \frac{25}{41} sin (x) - \frac{225}{41} cos (x)

y = c_{1} e^{\frac{( - 9 + 73 ) x}{2}} + c_{2} e^{- \frac{( 9 + 73 ) x}{2}} + \frac{25}{41} sin (x) - \frac{225}{41} cos (x)

y^{^{''}} + 4 x^{2} + 4 y = - 6

y^{^{''}} + 3 y^{^{'}} - 1 = 2 x^{2} + x

y^{^{''}} - 4 y = 24 cos (2 t)

y^{^{''}} + 2 y^{^{'}} + 10 y = 2 cos (x) + cos (3 x)

y^{^{''}} + 100 y^{^{'}} + 2500 y = 20