y^{''}+2y^'-15y=7e^{3t}+(1-2t)sin(6t)

Lösung

y^{^{''}} + 2 y^{^{'}} - 15 y = 7 e^{3 t} + (1 - 2 t) sin (6 t)

y = c_{1} e^{3 t} + c_{2} e^{- 5 t} + \frac{7 e ^{3 t} t}{8} + \frac{3436}{837225} cos (6 t) - \frac{5909}{279075} sin (6 t) + \frac{34 t sin ( 6 t ) + 8 t cos ( 6 t )}{915}

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) - 15 y = 7 e^{3 t} + (1 - 2 t) sin (6 t)

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 5 t} + \frac{7 e ^{3 t} t}{8} + \frac{3436}{837225} cos (6 t) - \frac{5909}{279075} sin (6 t) + \frac{34 t sin ( 6 t ) + 8 t cos ( 6 t )}{915}

y = c_{1} e^{3 t} + c_{2} e^{- 5 t} + \frac{7 e ^{3 t} t}{8} + \frac{3436}{837225} cos (6 t) - \frac{5909}{279075} sin (6 t) + \frac{34 t sin ( 6 t ) + 8 t cos ( 6 t )}{915}

y^{^{''}} + 2 y^{^{'}} + 2 y = g (t), y (0) = 8, y^{^{'}} (0) = 6

y^{^{''}} - 4 y = 1, y^{^{'}} (0) = 2

y^{^{''}} - 16 y = 19.2 e^{4 x} + 60 e^{x}

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

x^{^{''}} - 4 x^{^{'}} + 4 x = 4 e^{2 t}, x^{0} = - 1, x^{^{'}} 0 = - 4