y^{''}+2y^'+37y=4\H(t)

Lösung

y^{^{''}} + 2 y^{^{'}} + 37 y = 4 H (t)

y = e^{- t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + e^{- t} cos (6 t) \cdot \int - \frac{2 e ^{t} sin ( 6 t ) H ( t )}{3} d t + e^{- t} sin (6 t) \cdot \int \frac{2 e ^{t} cos ( 6 t ) H ( t )}{3} d t

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 37 y = 4 H (t)

Solve linear ODE:

y = e^{- t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + e^{- t} cos (6 t) \cdot \int - \frac{2 e ^{t} sin ( 6 t ) H ( t )}{3} d t + e^{- t} sin (6 t) \cdot \int \frac{2 e ^{t} cos ( 6 t ) H ( t )}{3} d t

y = e^{- t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + e^{- t} cos (6 t) \cdot \int - \frac{2 e ^{t} sin ( 6 t ) H ( t )}{3} d t + e^{- t} sin (6 t) \cdot \int \frac{2 e ^{t} cos ( 6 t ) H ( t )}{3} d t

5 y^{^{''}} + 4 y^{^{'}} + 8 y = 4 x - 1

4 y^{^{''}} + 20 y^{^{'}} + 169 y = e^{2 t}

(D^{3} + 8) y = x^{4} + 2 x + 1

y^{^{''}} - 6 y^{^{'}} + 13 y = 13

y^{^{''}} + 4 y = 16 t