What is the solution for (dy)/(dt)+3y=7,y(0)=1 ?

The solution for (dy)/(dt)+3y=7,y(0)=1 is y=-(4e^{-3t})/3+7/3

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(dy)/(dt)+3y=7,y(0)=1

\frac{d y}{d t} + 3 y = 7, y (0) = 1

y = - \frac{4 e ^{- 3 t}}{3} + \frac{7}{3}

Solution steps

\frac{d y}{d t} + 3 y = 7

Solve separable ODE:

y = - \frac{4 e ^{- 3 t}}{3} + \frac{7}{3}

y = - \frac{4 e ^{- 3 t}}{3} + \frac{7}{3}

e^{x} \cdot \frac{d y}{d x} = 1 + y^{2}

y^{^{'}} + x^{2} y = 0

\frac{d y}{d x} = e^{- y} (2 x - 4), y (5) = 0

(4 x - 1) d x - (6 y - 7) d y = 0

(2 y^{2} + x y^{3}) d x + (2 x y + x^{2} y^{2}) d y = 0

What is the solution for (dy)/(dt)+3y=7,y(0)=1 ?
The solution for (dy)/(dt)+3y=7,y(0)=1 is y=-(4e^{-3t})/3+7/3