(d^2-1)y=xsinh(x)

Lösung

(d^{2} - 1) \cdot y = x \cdot sinh (x)

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{x} x ^{2} + 2 e ^{- x} x ^{2} - 16 x sinh ( x ) - 6 e ^{- x} x + 6 e ^{x} x - 3 e ^{- x} - 3 e ^{x}}{16}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{x} x ^{2} + 2 e ^{- x} x ^{2} - 16 x sinh ( x ) - 6 e ^{- x} x + 6 e ^{x} x - 3 e ^{- x} - 3 e ^{x}}{16}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{x} x ^{2} + 2 e ^{- x} x ^{2} - 16 x sinh ( x ) - 6 e ^{- x} x + 6 e ^{x} x - 3 e ^{- x} - 3 e ^{x}}{16}

y^{^{''}} + y = 12 x

y^{^{''}} + 4 y = 2, e^{x} y (0) = 2, y^{^{'}} (0) = 1

(d^{2} - d - 2) y = 10 cos (x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 4, e^{3} t y (0) = 2, y^{^{'}} (0) = 7

(d^{2} + 4) y = sin^{2} (x)