What is the solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=5 ?

The solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=5 is y=6e^{-1/t+1}t-1

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t^2(dy)/(dt)-t=1+y+ty,y(1)=5

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 5

y = 6 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 = 6 e^{- \frac{1}{t} + 1} t - 1

y = 6 e^{- \frac{1}{t} + 1} t - 1

y = 0.01 x^{2} - 3 x + 229, y = 429 - 2 x, x = 0

\int \frac{1}{( 1 - sin ( x ) )} d x

\int 24 arctan (x) d x

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cos (x) \frac{d y}{d x} - sin (x) y = 0

What is the solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=5 ?
The solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=5 is y=6e^{-1/t+1}t-1