-1/9 y^{''}+2/3 y^'-y= t/(t+1)

Lösung

- \frac{1}{9} y^{^{''}} + \frac{2}{3} y^{^{'}} - y = \frac{t}{t + 1}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + e^{3 t} \cdot \int \frac{9 t ^{2}}{e ^{3 t} ( t + 1 )} d t + e^{3 t} t \cdot \int - \frac{9 t}{e ^{3 t} ( t + 1 )} d t

Schritte zur Lösung

- \frac{1}{9} y^{''} (t) + \frac{2}{3} y^{'} (t) - y = \frac{t}{t + 1}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + e^{3 t} \cdot \int \frac{9 t ^{2}}{e ^{3 t} ( t + 1 )} d t + e^{3 t} t \cdot \int - \frac{9 t}{e ^{3 t} ( t + 1 )} d t

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + e^{3 t} \cdot \int \frac{9 t ^{2}}{e ^{3 t} ( t + 1 )} d t + e^{3 t} t \cdot \int - \frac{9 t}{e ^{3 t} ( t + 1 )} d t

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

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

y^{^{''}} + y = 2 + t, y (0) = 1, y^{^{'}} (0) = 3

y^{^{''}} - 6 y^{^{'}} + 8 y = 4 e^{e - 2 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = - 80 sin (3 x) - 23 cos (3 x)