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

Lösung

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

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - \frac{11}{20} cos (2 x) + \frac{3}{20} sin (2 x) + cos^{2} (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - \frac{11}{20} cos (2 x) + \frac{3}{20} sin (2 x) + cos^{2} (x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - \frac{11}{20} cos (2 x) + \frac{3}{20} sin (2 x) + cos^{2} (x)

y^{^{''}} - 24 y = 2 x cos (5 x)

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 2 x^{2} + e^{x} + 2 x e^{x} + 4 e^{3 x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 7 e^{8 x}, y (0) = 0, y^{^{'}} (0) = 0

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

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