y^{''}-y=e^x+1

Lösung

y^{^{''}} - y = e^{x} + 1

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

Schritte zur Lösung

y^{''} (x) - y = e^{x} + 1

Solve linear ODE:

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

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

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

y^{^{''}} + 16 y = 32 sec (2 x)

(d^{2} - 2 d + 5) y = e^{x}

(d^{2} + 1) \cdot y = x \cdot cos (x)

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