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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

x \to - \infty lim (\frac{x ^{3} + x ^{2} - 3 x + 2}{x ^{2} - 3 x + 1})

\frac{d}{d x} (- \frac{1}{2} sin^{2} (x))

2 x^{2} - x

\int \frac{7 x ^{2} - 6 x + 8}{x ^{3} + 4 x} d x

\frac{d}{d x} (x sin (x y))

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