What is the solution for y^'+3y=1,3sin(t)y(0)=6 ?

The solution for y^'+3y=1,3sin(t)y(0)=6 is y=-(e^{-3t-c_{1}})/3+1/3

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y^'+3y=1,3sin(t)y(0)=6

y^{^{'}} + 3 y = 1, 3 sin (t) y (0) = 6

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

Solution steps

y^{'} (t) + 3 y = 1

Solve separable ODE:

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

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

What is the solution for y^'+3y=1,3sin(t)y(0)=6 ?
The solution for y^'+3y=1,3sin(t)y(0)=6 is y=-(e^{-3t-c_{1}})/3+1/3