y^{''}-4y^'+5y=e^{2x}csc(x)

Lösung

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2 x} csc (x)

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x)) - e^{2 x} x cos (x) + e^{2 x} ln (sin (x)) sin (x)

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 5 y = e^{2 x} csc (x)

Solve linear ODE:

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x)) - e^{2 x} x cos (x) + e^{2 x} ln (sin (x)) sin (x)

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x)) - e^{2 x} x cos (x) + e^{2 x} ln (sin (x)) sin (x)

y^{^{''}} - 2 y^{^{'}} + y = cos (3 x)

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

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

y^{^{'''}} + 6 y^{^{''}} + 12 y^{^{'}} + 8 y = 5 e^{- 2 x}

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 10 y = e^{2 x} + 20