y^{''}-y^'+y=3sin(t)-27e^{2t}

Lösung

y^{^{''}} - y^{^{'}} + y = 3 sin (t) - 27 e^{2 t}

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + 3 cos (t) - 9 e^{2 t}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) + y = 3 sin (t) - 27 e^{2 t}

Solve linear ODE:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + 3 cos (t) - 9 e^{2 t}

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + 3 cos (t) - 9 e^{2 t}