(d^2+3d+2)y=e^2x+sin(x)

Lösung

(d^{2} + 3 d + 2) y = e^{2} x + sin (x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{e ^{2} x}{2} - \frac{3 e ^{2}}{4} + \frac{1}{10} sin (x) - \frac{3}{10} cos (x)

Schritte zur Lösung

(d^{2} + 3 d + 2) y = e^{2} x + sin (x)

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{e ^{2} x}{2} - \frac{3 e ^{2}}{4} + \frac{1}{10} sin (x) - \frac{3}{10} cos (x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{e ^{2} x}{2} - \frac{3 e ^{2}}{4} + \frac{1}{10} sin (x) - \frac{3}{10} cos (x)

y^{^{''}} - 4 y^{^{'}} + 5 y = x^{2} e^{3} x

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

(d^{2} + 2) y = x^{2} e^{3} x

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

(d^{2} - 4 d - 12) \cdot y = (x - 1) \cdot e^{- 2 x}