(D^2-2D+1)y=cosh(x)

Lösung

(D^{2} - 2 D + 1) y = cosh (x)

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{8} e^{x} (- 2 e^{- 2 x} x - e^{- 2 x} + 2 x^{2}) + e^{x} x \cdot \int \frac{cosh ( x )}{e ^{x}} d x

Schritte zur Lösung

(D^{2} - 2 D + 1) y = cosh (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{8} e^{x} (- 2 e^{- 2 x} x - e^{- 2 x} + 2 x^{2}) + e^{x} x \cdot \int \frac{cosh ( x )}{e ^{x}} d x

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{8} e^{x} (- 2 e^{- 2 x} x - e^{- 2 x} + 2 x^{2}) + e^{x} x \cdot \int \frac{cosh ( x )}{e ^{x}} d x

y^{^{''}} - 2 y^{^{'}} - 24 y = 5 e^{3 x} + x^{2}

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{(2 x)} + x e^{(- 5 x)}

y^{^{''}} + y - 7 x sin (x) = 0

x^{^{''}} + 2 x^{^{'}} + x = e^{2 t}, x (0) = 2, x^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = - 2