(d^2y)/(dx^2)-4y=4sin(2x)-3e^2x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 sin (2 x) - 3 e^{2} x

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{1}{2} sin (2 x) + \frac{3 e ^{2} x}{4}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 sin (2 x) - 3 e^{2} x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{1}{2} sin (2 x) + \frac{3 e ^{2} x}{4}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{1}{2} sin (2 x) + \frac{3 e ^{2} x}{4}

12 y^{^{''}} - 5 y^{^{'}} - 3 y = e^{x}

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2} x (cos (x) - 6 sin (x))

y^{^{''}} + 4 y^{^{'}} = 4 - 4 e^{- 4 x}

y^{^{''}} - 9 y = e^{3 x}, y (0) = 3, y^{^{'}} (0) = 10

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} + cos (2 x)