3(d^2y)/(dx^2)+20(dy)/(dx)+25y=cos(2x)

Lösung

3 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 25 y = cos (2 x)

y = c_{1} e^{- \frac{5 x}{3}} + c_{2} e^{- 5 x} + \frac{40}{1769} sin (2 x) + \frac{13}{1769} cos (2 x)

Schritte zur Lösung

3 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 25 y = cos (2 x)

Solve linear ODE:

y = c_{1} e^{- \frac{5 x}{3}} + c_{2} e^{- 5 x} + \frac{40}{1769} sin (2 x) + \frac{13}{1769} cos (2 x)

y = c_{1} e^{- \frac{5 x}{3}} + c_{2} e^{- 5 x} + \frac{40}{1769} sin (2 x) + \frac{13}{1769} cos (2 x)

(D^{2} + 4 D + 5) y = e^{(- x)} + 15 x

y^{^{''}} + y = 2 cos (x), y^{^{'}} (π) = 0, y (0) = 0

(D^{2} + 1) y = cos^{2} (x)

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 9 y = x e^{- 3 x}

y^{^{''}} - y = t, y (0) = 0, y^{^{'}} (0) = 0