y^'+2y=2,6e^{-t}y(0)=3

Lösung

y^{^{'}} + 2 y = 2, 6 e^{- t} y (0) = 3

y = - e^{- 2 t - c_{1}} + 1

Schritte zur Lösung

y^{'} (t) + 2 y = 2

Solve separable ODE:

y = - e^{- 2 t - c_{1}} + 1

y = - e^{- 2 t - c_{1}} + 1

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

\frac{d y}{d x} = (2 x) (sec (y))

x^{2} y + y^{^{'}} = 3 x^{2}

y^{^{'}} = - 6 y + 12

\frac{d y}{d t} = \frac{t + 3 t ^{2}}{y ^{2}}