y^{''}-y=cosh(x),y(0)=2,y^'(0)=12

Lösung

y^{^{''}} - y = cosh (x), y (0) = 2, y^{^{'}} (0) = 12

y = (\frac{39}{8} + \frac{9}{4}) e^{x} - \frac{39}{8} e^{- x} + \frac{e ^{x} ( - e ^{- 2 x} + 2 x ) - e ^{- x} ( 2 x + e ^{2 x} )}{8}

Schritte zur Lösung

y^{''} (x) - y = cosh (x)

Solve linear ODE:

y = (\frac{39}{8} + \frac{9}{4}) e^{x} - \frac{39}{8} e^{- x} + \frac{e ^{x} ( - e ^{- 2 x} + 2 x ) - e ^{- x} ( 2 x + e ^{2 x} )}{8}

y = (\frac{39}{8} + \frac{9}{4}) e^{x} - \frac{39}{8} e^{- x} + \frac{e ^{x} ( - e ^{- 2 x} + 2 x ) - e ^{- x} ( 2 x + e ^{2 x} )}{8}

y^{^{''}} - y^{^{'}} - 6 y = 2 e^{4 t}

y^{^{''}} + 2 y^{^{'}} + 2 y = 3, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- x}

(4 d^{2} + 12 d + 9) y = 2022

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