y^{''}-6y^'+9y=t^2e^3

Lösung

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{2} e^{3}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3} t ^{2}}{9} + \frac{4 e ^{3} t}{27} + \frac{2 e ^{3}}{27}

Schritte zur Lösung

y^{''} (t) - 6 y^{'} (t) + 9 y = t^{2} e^{3}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3} t ^{2}}{9} + \frac{4 e ^{3} t}{27} + \frac{2 e ^{3}}{27}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3} t ^{2}}{9} + \frac{4 e ^{3} t}{27} + \frac{2 e ^{3}}{27}

y^{^{''}} - 2 y^{^{'}} + y = 2 x + x^{2} + sin (3 x)

y^{^{''}} + 4 y = cos (2 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} + 5 y = 4 e^{- t} cos (2 t)

y^{^{''}} - 5 y^{^{'}} + 4 y = e^{2 t}

y^{^{''}} - 6 y^{^{'}} + 8 y = 4 e^{4 x}