What is the solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=4 ?

The solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=4 is y=5e^{-1/t+1}t-1

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t^2(dy)/(dt)-t=1+y+ty,y(1)=4

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 4

y = 5 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 = 5 e^{- \frac{1}{t} + 1} t - 1

y = 5 e^{- \frac{1}{t} + 1} t - 1

\frac{\partial}{\partial x} (x ln (x y))

\int \frac{4}{x ^{2} + 9} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = 6 t^{2} e^{2 t}

f (x) = ln (e x)

x \to - 3 lim (\frac{2 x + 8}{x + 3})

What is the solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=4 ?
The solution for t^2(dy)/(dt)-t=1+y+ty,y(1)=4 is y=5e^{-1/t+1}t-1