What is the solution for (dy)/(dt)+ty=y,y(1)=3 ?

The solution for (dy)/(dt)+ty=y,y(1)=3 is y=3e^{t+(-t^2-1)/2}

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(dy)/(dt)+ty=y,y(1)=3

\frac{d y}{d t} + t y = y, y (1) = 3

y = 3 e^{t + \frac{- t ^{2} - 1}{2}}

Solution steps

\frac{d y}{d t} + t y = y

Solve separable ODE:

y = 3 e^{t + \frac{- t ^{2} - 1}{2}}

y = 3 e^{t + \frac{- t ^{2} - 1}{2}}

y^{^{'}} = e^{- y} \frac{x ^{5}}{7}

\frac{d y}{d x} = \frac{2 x}{( y + 1 )}

\frac{d y}{d x} = x y^{2} sin (x^{2})

\frac{d y}{d x} + (y - \frac{1}{y}) x = 0

What is the solution for (dy)/(dt)+ty=y,y(1)=3 ?
The solution for (dy)/(dt)+ty=y,y(1)=3 is y=3e^{t+(-t^2-1)/2}