What is the solution for (dy)/(dt)+2y=3,y(0)=1 ?

The solution for (dy)/(dt)+2y=3,y(0)=1 is y=-(e^{-2t})/2+3/2

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(dy)/(dt)+2y=3,y(0)=1

\frac{d y}{d t} + 2 y = 3, y (0) = 1

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

Solution steps

\frac{d y}{d t} + 2 y = 3

Solve separable ODE:

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

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

\frac{d y}{d x} + y cos (x) = 6 cos (x)

e^{x} d x - (1 + e^{x}) y d y = 0

\frac{x ^{2}}{y ^{2} - 3} \frac{d y}{d x} = \frac{1}{2 y}

sin (x) cos (y) d x + cos (x) sin (y) d y = 0

3 x^{2} y^{2} \frac{d y}{d x} = 2 x - 1

What is the solution for (dy)/(dt)+2y=3,y(0)=1 ?
The solution for (dy)/(dt)+2y=3,y(0)=1 is y=-(e^{-2t})/2+3/2