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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 9} e^{5 t}

y^{^{''}} - 14 \cdot y^{^{''}} + 45 \cdot y^{^{'}} = 32 e^{x}

y^{^{''}} - y^{^{'}} - 6 y = 4 t e^{3} t, y (0) = - 5, y^{^{'}} (0) = - 3

y^{^{''}} + y^{^{'}} - 2 y = - 4, y (0) = 2, y^{^{'}} (0) = 3

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