10x^{''}+45x^'+2500x=180cos(7pi)

Lösung

10 x^{^{''}} + 45 x^{^{'}} + 2500 x = 180 cos (7 π)

x = e^{- \frac{9 t}{4}} (c_{1} cos (\frac{3919 t}{4}) + c_{2} sin (\frac{3919 t}{4})) - \frac{9}{125}

Schritte zur Lösung

10 x^{''} (t) + 45 x^{'} (t) + 2500 x = 180 cos (7 π)

Solve linear ODE:

x = e^{- \frac{9 t}{4}} (c_{1} cos (\frac{3919 t}{4}) + c_{2} sin (\frac{3919 t}{4})) - \frac{9}{125}

x = e^{- \frac{9 t}{4}} (c_{1} cos (\frac{3919 t}{4}) + c_{2} sin (\frac{3919 t}{4})) - \frac{9}{125}

y^{^{''}} + 7 y^{^{'}} + 12 y = 5 x

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} - 64 y = 7 e^{8 x}

y^{^{''}} - 11 y^{^{'}} + 24 y = 2, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 10 y = 10 x + 2

y^{^{'''}} + 3 y^{^{''}} - 7 y^{^{'}} + 2 y = 3 x + 10 sin (x)