What is the solution for (y^')/(e^t)=y^2-5y+6 ?

The solution for (y^')/(e^t)=y^2-5y+6 is y=-(2e^{e^t+c_{1}})/(1-e^{e^t+c_{1)}}+3/(1-e^{e^t+c_{1)}}

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

\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}}}

Solution steps

\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}}}

What is the solution for (y^')/(e^t)=y^2-5y+6 ?
The solution for (y^')/(e^t)=y^2-5y+6 is y=-(2e^{e^t+c_{1}})/(1-e^{e^t+c_{1)}}+3/(1-e^{e^t+c_{1)}}