y^{''}+4y=t^2sin(2t)+(6t+7)cos(2t)

Lösung

y^{^{''}} + 4 y = t^{2} sin (2 t) + (6 t + 7) cos (2 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 8 t ^{3} cos ( 2 t ) + 78 t ^{2} sin ( 2 t ) + 39 t cos ( 2 t ) + 168 t sin ( 2 t )}{96}

Schritte zur Lösung

y^{''} (t) + 4 y = t^{2} sin (2 t) + (6 t + 7) cos (2 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 8 t ^{3} cos ( 2 t ) + 78 t ^{2} sin ( 2 t ) + 39 t cos ( 2 t ) + 168 t sin ( 2 t )}{96}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 8 t ^{3} cos ( 2 t ) + 78 t ^{2} sin ( 2 t ) + 39 t cos ( 2 t ) + 168 t sin ( 2 t )}{96}

x^{^{''}} + 25 x = t^{2} + t

y^{^{''}} + 6 y^{^{'}} + 8 y = 3 t e^{- 4 t}

3 x^{^{''}} + 48 x = 120 e^{- 4 t} (cos (4 t))

so l v e f or D, D (t) = \frac{100 ln ( t + 2 )}{t - 2}

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 24 y = 4 e^{6 t}