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

Lösung

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

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

y^{^{''}} - y^{^{'}} = 3 - 2 x, y (0) = - 1, y^{^{'}} (0) = - 1

y^{^{''}} - 25 y = e^{x}

y^{^{''}} - 14 y^{^{'}} + 45 y = 360 x^{2} - 224 x + 16

y^{^{''}} + 5 y^{^{'}} + 4 y = sec (x)

y^{^{''}} + 4 y = cos (t), y^{^{'}} (0) = 1, y (0) = 1