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

Lösung

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

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- x} - \frac{1}{10} sin (x) - \frac{3}{10} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- x} - \frac{1}{10} sin (x) - \frac{3}{10} cos (x)

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- x} - \frac{1}{10} sin (x) - \frac{3}{10} cos (x)

y^{^{''}} + 5 y^{^{'}} + 6 y = 3

x^{^{''}} + 4 x = cos (t)

y^{^{''}} + 9 y = cos (8 x)

(d^{2} - 2 d + 1) y = x^{2} e^{2} x

y^{^{''}} - y^{^{'}} - 12 y = e^{2 x} + e^{x - 2}