y^{''}+y^'-6y=-3sin(x)+4e^{2x}

Lösung

y^{^{''}} + y^{^{'}} - 6 y = - 3 sin (x) + 4 e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{21}{50} sin (x) + \frac{3}{50} cos (x) + \frac{4 e ^{2 x} x}{5}

Schritte zur Lösung

y^{''} (x) + y^{'} (x) - 6 y = - 3 sin (x) + 4 e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{21}{50} sin (x) + \frac{3}{50} cos (x) + \frac{4 e ^{2 x} x}{5}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{21}{50} sin (x) + \frac{3}{50} cos (x) + \frac{4 e ^{2 x} x}{5}

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} + 4 y = t e^{2 t}

y^{^{''}} - 25 y = sinh (5 x)

y^{^{''}} + y^{^{'}} - 12 y = e^{x} + e^{2 x} - 1

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

y^{^{''}} - y^{^{'}} = e^{2 x}, y (0) = 0, y (1) = 0