2(d^2y)/(dx^2)+(dy)/(dx)+3y=e^{2x}

Lösung

2 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 3 y = e^{2 x}

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{23 x}{4}) + c_{2} sin (\frac{23 x}{4})) + \frac{1}{13} e^{2 x}

Schritte zur Lösung

2 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 3 y = e^{2 x}

Solve linear ODE:

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{23 x}{4}) + c_{2} sin (\frac{23 x}{4})) + \frac{1}{13} e^{2 x}

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{23 x}{4}) + c_{2} sin (\frac{23 x}{4})) + \frac{1}{13} e^{2 x}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 2

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 4

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 6

y^{^{''}} + 7 y^{^{'}} + 6 y = 6 cos (5 t + 1.5708) H (t)

y^{^{''}} - y^{^{'}} - 2 y = sin (3 t), y (0) = 1, y (0) = - 1