(y^')/(e^t)=y^2-5y+6

Lösung

\frac{y ^{^{'}}}{e ^{t}} = y^{2} - 5 y + 6

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

Schritte zur Lösung

\frac{y ^{'} ( t )}{e ^{t}} = y^{2} - 5 y + 6

Solve separable ODE:

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

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

y^{(4)} - 8 y^{^{'}} = 0

y^{^{'}} = \frac{1}{sin ( y )}

\frac{d x}{d t} = 8 x t^{4}

d y = \frac{( y + 7 )}{( x + 4 )} d x

y^{^{'}} = (x + 1) e^{y}