What is the solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=7 ?

The solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=7 is y=8e^{-1/t+1}t-1

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t^2(dy)/(dt)-t=1+y+ty,y(1)=7

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 7

y = 8 e^{- \frac{1}{t} + 1} t - 1

Solution steps

t^{2} \frac{d y}{d t} - t = 1 + y + t y

Solve separable ODE:

y = 8 e^{- \frac{1}{t} + 1} t - 1

y = 8 e^{- \frac{1}{t} + 1} t - 1

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What is the solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=7 ?
The solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=7 is y=8e^{-1/t+1}t-1