y^{''}-36y^'=-42e^{-5t},y(0)=7,y^'(0)=0

Lösung

y^{^{''}} - 36 y^{^{'}} = - 42 e^{- 5 t}, y (0) = 7, y^{^{'}} (0) = 0

y = (- \frac{217}{30} + \frac{1477}{205}) e^{36 t} + \frac{217}{30} - \frac{42}{205} e^{- 5 t}

Schritte zur Lösung

y^{''} (t) - 36 y^{'} (t) = - 42 e^{- 5 t}

Solve linear ODE:

y = (- \frac{217}{30} + \frac{1477}{205}) e^{36 t} + \frac{217}{30} - \frac{42}{205} e^{- 5 t}

y = (- \frac{217}{30} + \frac{1477}{205}) e^{36 t} + \frac{217}{30} - \frac{42}{205} e^{- 5 t}

2 \frac{d ^{2} y}{d t ^{2}} + 20 \frac{d y}{d t} + 50 = 8 \cdot (t)

y^{^{''}} - y = 2^{x}

x^{^{''}} - 3 x^{^{'}} + 2 x = 2 sin (t) - 6 cos (t)

y^{^{''}} - 7 y^{^{'}} + 12 y = 6 e^{x}

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 x^{2} + x - 2