y^{''}-4y=sinh(2x)

Lösung

y^{^{''}} - 4 y = sinh (2 x)

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x} sinh ( 2 x )}{4} d x + e^{- 2 x} \cdot \int - \frac{e ^{2 x} sinh ( 2 x )}{4} d x

Schritte zur Lösung

y^{''} (x) - 4 y = sinh (2 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x} sinh ( 2 x )}{4} d x + e^{- 2 x} \cdot \int - \frac{e ^{2 x} sinh ( 2 x )}{4} d x

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{e ^{- 2 x} sinh ( 2 x )}{4} d x + e^{- 2 x} \cdot \int - \frac{e ^{2 x} sinh ( 2 x )}{4} d x

y^{^{''}} + 6 y^{^{'}} + 5 y = 36 e^{x}, y (0) = - 2

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{t}, y (0) = 1, y (0) = - 1

y^{^{''}} + y = e^{t}

y^{^{''}} - 2 y^{^{'}} + 2 y = \frac{e ^{x}}{cos ( x )}

y^{^{'''}} + 9 y^{^{'}} = - 18 t