(d^2y)/(dx^2)-y=cosh(x)+x

Lösung

\frac{d ^{2} y}{d x ^{2}} - y = cosh (x) + x

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{2 x} x - 8 e ^{x} x - 2 x - e ^{2 x} - 1}{8 e ^{x}}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - y = cosh (x) + x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{2 x} x - 8 e ^{x} x - 2 x - e ^{2 x} - 1}{8 e ^{x}}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{2 x} x - 8 e ^{x} x - 2 x - e ^{2 x} - 1}{8 e ^{x}}

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

y^{^{''''}} + 8 y^{^{''}} + 16 y = 64 + cos (4 t)

\frac{d ^{2} x}{d t ^{2}} + 25 x = 30 cos (6 t)

y^{^{''}} - 6 y^{^{'}} + 5 y = 3 x + e^{x}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} + y = 9 - e^{2 x}, y (0) = 0, y^{^{'}} (0) = 1