(d^2y)/(dx^2)-5(dy)/(dx)+4y=tan(x)

Lösung

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 4 y = tan (x)

y = c_{1} e^{4 x} + c_{2} e^{x} + e^{4 x} \cdot \int \frac{tan ( x )}{3 e ^{4 x}} d x + e^{x} \cdot \int - \frac{tan ( x )}{3 e ^{x}} d x

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 4 y = tan (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{x} + e^{4 x} \cdot \int \frac{tan ( x )}{3 e ^{4 x}} d x + e^{x} \cdot \int - \frac{tan ( x )}{3 e ^{x}} d x

y = c_{1} e^{4 x} + c_{2} e^{x} + e^{4 x} \cdot \int \frac{tan ( x )}{3 e ^{4 x}} d x + e^{x} \cdot \int - \frac{tan ( x )}{3 e ^{x}} d x

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

y^{^{''}} - y^{^{'}} - 6 y = 50 e^{- 2 x}

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- 4 x}, y (0) = - 2, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} - 3 y = 6 e^{- 2 x}

y^{^{''}} + y = 2 x e^{3 x}