y^{''}-y^'-6y=5t,y(0)=3,y^'(0)=1

Lösung

y^{^{''}} - y^{^{'}} - 6 y = 5 t, y (0) = 3, y^{^{'}} (0) = 1

y = (- \frac{27}{20} + \frac{103}{36}) e^{3 t} + \frac{27}{20} e^{- 2 t} - \frac{5 t}{6} + \frac{5}{36}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 6 y = 5 t

Solve linear ODE:

y = (- \frac{27}{20} + \frac{103}{36}) e^{3 t} + \frac{27}{20} e^{- 2 t} - \frac{5 t}{6} + \frac{5}{36}

y = (- \frac{27}{20} + \frac{103}{36}) e^{3 t} + \frac{27}{20} e^{- 2 t} - \frac{5 t}{6} + \frac{5}{36}

so l v e f or D, D (x) = x^{8} - 4^{4}

x^{^{''}} + 2 x^{^{'}} + 3 x = t^{2} + 4 t

y^{^{''}} - 2 y^{^{'}} + y = (e^{x} - 1)^{2}, y (0) = 0, y^{^{'}} (0) = 1

2 y^{^{''}} + 3 y^{^{'}} + y = g t

y^{^{''}} - y = 2 t, y (0) = - 2 t