y^{''}-3y^'+2y=1+2e^{3t}

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = 1 + 2 e^{3 t}

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{2} + e^{3 t}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) + 2 y = 1 + 2 e^{3 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{2} + e^{3 t}

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{2} + e^{3 t}

l a pl a ce t r an s f or m t^{2} sin (\frac{1}{2} t)

n = 0 \sum \infty n^{n} x^{n}

x \to 0 lim (\frac{3 - 3 cos ( x )}{sin ^{2} ( x )})

d er i v a t i v e f (x) = \frac{11}{( 1 - x ) ^{2}}

\int sin^{3} (2 x) d x